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Nature of Operations and Summary of Significant Accounting Policies - Schedule of Changes in Allowance for Credit Losses (Detail) - USD ($)	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023
Receivables [Abstract]
Balance, beginning of year	$ 545,000	$ 370,000
Provision for credit losses	0	290,000
Provision for estimated returns and allowances	155,000	335,000
Uncollectible accounts written off	(20,000)	(65,000)
Returns and allowances issued	(290,000)	(385,000)
Balance, end of year	$ 390,000	$ 545,000

X

- Definition

Allowance for doubtful accounts receivable returns and allowances issued.

+ References

No definition available.

+ Details

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Namespace Prefix:	genc_
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Balance Type:	debit
Period Type:	duration

X

- Definition

Provision for doubtful accounts estimated returns and allowances.

+ References

No definition available.

+ Details

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Namespace Prefix:	genc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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X

- Definition

Amount of allowance for credit loss on accounts receivable, classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479344/326-20-45-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481962/310-10-50-4

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Amount of direct write-downs of accounts receivable charged against the allowance.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 13
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-13

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Period Type:	duration

X

- Definition

Amount of expense (reversal of expense) for expected credit loss on accounts receivable.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 13
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-13

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(5))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

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- References

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