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Stock-Based Compensation (Details) (USD $)
In Millions, except Share data, unless otherwise specified
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Stock-based compensation      
Compensation expense related to the Plan $ 12.8us-gaap_AllocatedShareBasedCompensationExpense $ 9.8us-gaap_AllocatedShareBasedCompensationExpense $ 6.8us-gaap_AllocatedShareBasedCompensationExpense
Restricted Stock      
Stock-based compensation      
Period over which forfeiture and non-transferable restrictions lapse 4 years    
Percentage over which unrecognized compensation cost is expected to be recognized year one 15.00%pag_ShareBasedCompensationArrangementByShareBasedPaymentAwardForfeitureAndNonTransferableRestrictionExpirationPercentageYearOne
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Percentage over which unrecognized compensation cost is expected to be recognized year two 15.00%pag_ShareBasedCompensationArrangementByShareBasedPaymentAwardForfeitureAndNonTransferableRestrictionExpirationPercentageYearTwo
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Percentage over which unrecognized compensation cost is expected to be recognized year three 20.00%pag_ShareBasedCompensationArrangementByShareBasedPaymentAwardForfeitureAndNonTransferableRestrictionExpirationPercentageYearThree
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Percentage over which unrecognized compensation cost is expected to be recognized year four 50.00%pag_ShareBasedCompensationArrangementByShareBasedPaymentAwardForfeitureAndNonTransferableRestrictionExpirationPercentageYearFour
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Unrecognized compensation cost related to the restricted stock 20.0us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Shares      
Balance at the beginning of the period (in shares) 1,168,200us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Granted (in shares) 314,677us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
448,026us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
431,339us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
Vested (in shares) (373,450)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Forfeited (in shares) (7,042)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Balance at the end of the period (in shares) 1,102,385us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
1,168,200us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Weighted Average Grant-Date Fair value      
Balance at the beginning of the period (in dollars per share) $ 23.75us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Granted (in dollars per share) $ 44.03us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Vested (in dollars per share) $ 20.00us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Forfeited (in dollars per share) $ 27.12us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Balance at the end of the period (in dollars per share) $ 30.78us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 23.75us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Aggregate Intrinsic Value      
Balance at the end of the period (in dollars) $ 54.1us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
2012 Plan      
Stock-based compensation      
Maximum term of options 3 years    
Number of shares of common stock available for grant under the plan 2,000,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= pag_Plan2012Member
   
Number of shares of common stock available for grant under the plan 1,121,582us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_PlanNameAxis
= pag_Plan2012Member