Leases - Additional Information (Details) $ in Millions	Feb. 01, 2025 USD ($)
Operating Leased Assets [Line Items]
Operating lease, lease not yet commenced with right of use liabilities	$ 27.9
Minimum
Operating Leased Assets [Line Items]
Operating lease, lease not yet commenced, term of contract	1 year
Maximum
Operating Leased Assets [Line Items]
Operating lease, lease not yet commenced, term of contract	11 years
United States, Puerto Rico and Canada
Operating Leased Assets [Line Items]
Lease term	10 years
United Kingdom and ROI \| Minimum
Operating Leased Assets [Line Items]
Lease term	10 years
United Kingdom and ROI \| Maximum
Operating Leased Assets [Line Items]
Lease term	15 years

Lessee operating lease lease not yet commenced with estimated right of use liability.

No definition available.

Name:	gco_LesseeOperatingLeaseLeaseNotYetCommencedWithEstimatedRightOfUseLiability
Namespace Prefix:	gco_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Term of lessee's operating lease not yet commenced, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-3

+ Details

Name:	us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedTermOfContract1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Term of lessee's operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-3

+ Details

Name:	us-gaap_LesseeOperatingLeaseTermOfContract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Details

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Namespace Prefix:
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- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
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- Details

Name:	srt_StatementGeographicalAxis=gco_UnitedStatesPuertoRicoAndCanadaMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_StatementGeographicalAxis=gco_UnitedKingdomAndTheRepublicOfIrelandMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: