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Balance Sheet Accounts and Supplemental Disclosures - Schedule of Other Current Liabilities (Details) (USD $)
In Millions, unless otherwise specified
Nov. 30, 2014
Nov. 30, 2013
Schedule Of Other Liabilities [Line Items]    
Accrued compensation and employee benefits $ 96.1us-gaap_AccruedEmployeeBenefitsCurrent $ 97.4us-gaap_AccruedEmployeeBenefitsCurrent
Taxes Payable 14.1us-gaap_TaxesPayableCurrentAndNoncurrent 0us-gaap_TaxesPayableCurrentAndNoncurrent
Income taxes   0us-gaap_TaxesPayableCurrent
Interest payable 14.6us-gaap_InterestPayableCurrent 12.3us-gaap_InterestPayableCurrent
Contract loss provisions 13.4us-gaap_ProvisionForLossOnContracts 10.5us-gaap_ProvisionForLossOnContracts
Other 71.6gy_MiscellaneousOtherLiabilitiesCurrent 65.4gy_MiscellaneousOtherLiabilitiesCurrent
Other current liabilities 221.7us-gaap_OtherLiabilitiesCurrent 206.0us-gaap_OtherLiabilitiesCurrent
UTC [Member]    
Schedule Of Other Liabilities [Line Items]    
Payable to UTC primarily for Transition Service Agreements $ 11.9us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent
/ us-gaap_CounterpartyNameAxis
= gy_UnitedTechnologiesCorporationMember
$ 20.4us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent
/ us-gaap_CounterpartyNameAxis
= gy_UnitedTechnologiesCorporationMember