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Property and Equipment - Additional Information (Detail) - USD ($)	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020
Property, Plant and Equipment [Abstract]
Property and equipment (fully depreciated assets)	$ 19,374,000	$ 14,300,000

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- Definition

Property and equipment (fully depreciated assets).

+ References

No definition available.

+ Details

Name:	genc_PropertyAndEquipmentFullyDepreciatedAssets
Namespace Prefix:	genc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

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- References

No definition available.

+ Details

Name:	us-gaap_PropertyPlantAndEquipmentAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration