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Nature of Operations and Summary of Significant Accounting Policies - Schedule of Changes in Allowance for Slow Moving and Obsolete Inventories (Detail) - USD ($)	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023
Inventory Disclosure [Abstract]
Balance, beginning of year	$ 9,813,000	$ 8,192,000
Charged to cost of sales	3,834,000	2,147,000
Disposal of inventory, net of recoveries	(316,000)	(526,000)
Balance, end of year	$ 13,331,000	$ 9,813,000

X

- Definition

Inventory reserve charged to costs of sales.

+ References

No definition available.

+ Details

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

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- References

No definition available.

+ Details

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

X

- Definition

Amount by which inventory stated at last-in first-out (LIFO) is less than (in excess of) inventory stated at other inventory cost methods.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(6)(c))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

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Namespace Prefix:	us-gaap_
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Balance Type:	credit
Period Type:	instant

X

- Definition

Amount of loss from reductions in inventory due to subsequent measurement adjustments, including, but not limited to, physical deterioration, obsolescence, or changes in price levels.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 330
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483080/330-10-50-2

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