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Nature of Operations and Summary of Significant Accounting Policies - Schedule of Changes in Accrual for Warranty and Related Costs (Detail) - USD ($)	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023
Product Warranty Liability [Abstract]
Balance, beginning of year	$ 366,000	$ 244,000
Warranties issued	287,000	523,000
Warranties settled	(330,000)	(401,000)
Balance, end of year	$ 323,000	$ 366,000

X

- Definition

Product warranty liability.

+ References

No definition available.

+ Details

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

X

- Definition

Carrying value as of the balance sheet date of obligations incurred through that date and payable for estimated claims under standard and extended warranty protection rights granted to customers.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(15)(5))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 460
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482425/460-10-50-4

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 460
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (c)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482425/460-10-50-8

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 460
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (c)(5)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482425/460-10-50-8

+ Details

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

X

- Definition

Amount of decrease in the standard and extended product warranty accrual from payments made in cash or in kind to satisfy claims under the terms of the standard and extended product warranty.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 460
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (c)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482425/460-10-50-8

+ Details

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Balance Type:	debit
Period Type:	duration

X

- Definition

Amount of increase in the standard and extended product warranty accrual from warranties issued.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 460
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (c)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482425/460-10-50-8

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