Finite Group Databasebeta

← Group #72269095

Character table — Group #72269095

Order 20736.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size189121818182436864729614414414419228897281108162162162216324129610814421621621628843218144162216324324324432648181441622163243243244326481814416221632432432443264824192216288432432432576864362883244326486486488641296
order1322488643366122424612262248864262248864412444881248248888824882488888248666612242461241244488124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111-1-11-111111-1-11-111111-1-11-111111-1-11-111111-1-11-111111-1-11-111111-1-11-111111-1-11-111111-1-11-1
χ3111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1
χ4111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11
χ52220-200002220-200002220-200002220-200002220-200002220-200002220-200002220-200002220-20000
χ622-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i200
χ722-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i200
χ88-102000-108-102000-108-102000-108-102000-108-102000-108-102000-108-102000-108-102000-108-102000-10
χ98-10-2000108-10-2000108-10-2000108-10-2000108-10-2000108-10-2000108-10-2000108-10-2000108-10-200010
χ10111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1
χ1111111-1-11-111111-1-11-111111-1-11-111111-1-11-111111-1-11-1-1-1-1-1-111-11-1-1-1-1-111-1111111-1-11-1-1-1-1-1-111-11
χ12111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1111-1111-1-1-1-1-11-1-1-111-1-1-11-1-1-111111-1111-1-1-1-1-11-1-1-111
χ13111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11-1-1-11-1111-1-1-1-11-1111-1111-11-1-1-11-1-1-11-1111-1
χ142220-200002220-200002220-200002220-200002220-20000-2-2-2020000-2-2-20200002220-20000-2-2-2020000
χ1522-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i20022-200i2−i200-2-2200−i2i200-2-2200−i2i20022-200i2−i200-2-2200−i2i200
χ1622-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i20022-200−i2i200-2-2200i2−i200-2-2200i2−i20022-200−i2i200-2-2200i2−i200
χ178-102000-108-102000-108-102000-108-102000-108-102000-10-810-200010-810-2000108-102000-10-810-200010
χ188-10-2000108-10-2000108-10-2000108-10-2000108-10-200010-8102000-10-8102000-108-10-200010-8102000-10
χ19111111111111111111111111111-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2011111-1-11-111111-1-11-111111-1-11-1-1-1-1-1-111-1111111-1-11-111111-1-11-111111-1-11-1-1-1-1-1-111-11-1-1-1-1-111-11
χ21111-1111-1-1111-1111-1-1111-1111-1-1-1-1-11-1-1-111111-1111-1-1111-1111-1-1111-1111-1-1-1-1-11-1-1-111-1-1-11-1-1-111
χ22111-11-1-1-11111-11-1-1-11111-11-1-1-11-1-1-11-1111-1111-11-1-1-11111-11-1-1-11111-11-1-1-11-1-1-11-1111-1-1-1-11-1111-1
χ232220-200002220-200002220-20000-2-2-20200002220-200002220-200002220-20000-2-2-2020000-2-2-2020000
χ2422-200i2−i20022-200i2−i20022-200i2−i200-2-2200−i2i20022-200i2−i20022-200i2−i20022-200i2−i200-2-2200−i2i200-2-2200−i2i200
χ2522-200−i2i20022-200−i2i20022-200−i2i200-2-2200i2−i20022-200−i2i20022-200−i2i20022-200−i2i200-2-2200i2−i200-2-2200i2−i200
χ268-102000-108-102000-108-102000-10-810-2000108-102000-108-102000-108-102000-10-810-200010-810-200010
χ278-10-2000108-10-2000108-10-200010-8102000-108-10-2000108-10-2000108-10-200010-8102000-10-8102000-10
χ28111111111111111111111111111-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111
χ2911111-1-11-111111-1-11-111111-1-11-1-1-1-1-1-111-1111111-1-11-1-1-1-1-1-111-11-1-1-1-1-111-11-1-1-1-1-111-1111111-1-11-1
χ30111-1111-1-1111-1111-1-1111-1111-1-1-1-1-11-1-1-111111-1111-1-1-1-1-11-1-1-111-1-1-11-1-1-111-1-1-11-1-1-111111-1111-1-1
χ31111-11-1-1-11111-11-1-1-11111-11-1-1-11-1-1-11-1111-1111-11-1-1-11-1-1-11-1111-1-1-1-11-1111-1-1-1-11-1111-1111-11-1-1-11
χ322220-200002220-200002220-20000-2-2-20200002220-20000-2-2-2020000-2-2-2020000-2-2-20200002220-20000
χ3322-200i2−i20022-200i2−i20022-200i2−i200-2-2200−i2i20022-200i2−i200-2-2200−i2i200-2-2200−i2i200-2-2200−i2i20022-200i2−i200
χ3422-200−i2i20022-200−i2i20022-200−i2i200-2-2200i2−i20022-200−i2i200-2-2200i2−i200-2-2200i2−i200-2-2200i2−i20022-200−i2i200
χ358-102000-108-102000-108-102000-10-810-2000108-102000-10-810-200010-810-200010-810-2000108-102000-10
χ368-10-2000108-10-2000108-10-200010-8102000-108-10-200010-8102000-10-8102000-10-8102000-108-10-200010
χ37222222222222222222222222222000000000-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ3822222-2-22-222222-2-22-222222-2-22-2000000000-2-2-2-2-222-22000000000000000000000000000000000000
χ39222-2222-2-2222-2222-2-2222-2222-2-2000000000-2-2-22-2-2-222000000000000000000000000000000000000
χ40222-22-2-2-22222-22-2-2-22222-22-2-2-22000000000-2-2-22-2222-2000000000000000000000000000000000000
χ414440-400004440-400004440-40000000000000-4-4-4040000000000000000000000000000000000000000
χ4244-4002i2−2i20044-4002i2−2i20044-4002i2−2i200000000000-4-4400−2i22i200000000000000000000000000000000000000
χ4344-400−2i22i20044-400−2i22i20044-400−2i22i200000000000-4-44002i2−2i200000000000000000000000000000000000000
χ4416-204000-2016-204000-2016-204000-20000000000-1620-400020000000000000000000000000000000000000
χ4516-20-40002016-20-40002016-20-400020000000000-16204000-20000000000000000000000000000000000000
χ46222222222222222222-2-2-2-2-2-2-2-2-2000000000000000000i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2−i2000000000000000000
χ4722222-2-22-222222-2-22-2-2-2-2-2-222-22000000000000000000i2i2i2i2i2−i2−i2i2−i2−i2−i2−i2−i2−i2i2i2−i2i2000000000000000000
χ48222-2222-2-2222-2222-2-2-2-2-22-2-2-222000000000000000000i2i2i2−i2i2i2i2−i2−i2−i2−i2−i2i2−i2−i2−i2i2i2000000000000000000
χ49222-22-2-2-22222-22-2-2-22-2-2-22-2222-2000000000000000000i2i2i2−i2i2−i2−i2−i2i2−i2−i2−i2i2−i2i2i2i2−i2000000000000000000
χ504440-400004440-40000-4-4-40400000000000000000000002i22i22i20−2i20000−2i2−2i2−2i202i20000000000000000000000
χ5144-4002i2−2i20044-4002i2−2i200-4-4400−2i22i2000000000000000000002i22i2−2i200-2200−2i2−2i22i2002-200000000000000000000
χ5244-400−2i22i20044-400−2i22i200-4-44002i2−2i2000000000000000000002i22i2−2i2002-200−2i2−2i22i200-2200000000000000000000
χ5316-204000-2016-204000-20-1620-4000200000000000000000008i2−i202i2000−i20−8i2i20−2i2000i20000000000000000000
χ5416-20-40002016-20-400020-16204000-200000000000000000008i2−i20−2i2000i20−8i2i202i2000−i20000000000000000000
χ55222222222222222222-2-2-2-2-2-2-2-2-2000000000000000000−i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2i2i2i2000000000000000000
χ5622222-2-22-222222-2-22-2-2-2-2-2-222-22000000000000000000−i2−i2−i2−i2−i2i2i2−i2i2i2i2i2i2i2−i2−i2i2−i2000000000000000000
χ57222-2222-2-2222-2222-2-2-2-2-22-2-2-222000000000000000000−i2−i2−i2i2−i2−i2−i2i2i2i2i2i2−i2i2i2i2−i2−i2000000000000000000
χ58222-22-2-2-22222-22-2-2-22-2-2-22-2222-2000000000000000000−i2−i2−i2i2−i2i2i2i2−i2i2i2i2−i2i2−i2−i2−i2i2000000000000000000
χ594440-400004440-40000-4-4-4040000000000000000000000−2i2−2i2−2i202i200002i22i22i20−2i20000000000000000000000
χ6044-4002i2−2i20044-4002i2−2i200-4-4400−2i22i200000000000000000000−2i2−2i22i2002-2002i22i2−2i200-2200000000000000000000
χ6144-400−2i22i20044-400−2i22i200-4-44002i2−2i200000000000000000000−2i2−2i22i200-22002i22i2−2i2002-200000000000000000000
χ6216-204000-2016-204000-20-1620-400020000000000000000000−8i2i20−2i2000i208i2−i202i2000−i20000000000000000000
χ6316-20-40002016-20-400020-16204000-20000000000000000000−8i2i202i2000−i208i2−i20−2i2000i20000000000000000000
χ64888888888-1-1-1-1-1-1-1-1-1000000000222222222000000000000000000000000000-1-1-1-1-1-1-1-1-1000000000
χ6588888-8-88-8-1-1-1-1-111-1100000000022222-2-22-2000000000000000000000000000-1-1-1-1-111-11000000000
χ66888-8888-8-8-1-1-11-1-1-111000000000222-2222-2-2000000000000000000000000000-1-1-11-1-1-111000000000
χ67888-88-8-8-88-1-1-11-1111-1000000000222-22-2-2-22000000000000000000000000000-1-1-11-1111-1000000000
χ681616160-160000-2-2-20200000000000004440-40000000000000000000000000000000-2-2-2020000000000000
χ691616-16008i2−8i200-2-2200−i2i20000000000044-4002i2−2i200000000000000000000000000000-2-2200−i2i200000000000
χ701616-1600−8i28i200-2-2200i2−i20000000000044-400−2i22i200000000000000000000000000000-2-2200i2−i200000000000
χ7164-8016000-80-810-20001000000000016-204000-20000000000000000000000000000-810-200010000000000
χ7264-80-1600080-8102000-1000000000016-20-400020000000000000000000000000000-8102000-10000000000
χ73888888888-1-1-1-1-1-1-1-1-1000000000-2-2-2-2-2-2-2-2-2000000000000000000000000000111111111000000000
χ7488888-8-88-8-1-1-1-1-111-11000000000-2-2-2-2-222-2200000000000000000000000000011111-1-11-1000000000
χ75888-8888-8-8-1-1-11-1-1-111000000000-2-2-22-2-2-222000000000000000000000000000111-1111-1-1000000000
χ76888-88-8-8-88-1-1-11-1111-1000000000-2-2-22-2222-2000000000000000000000000000111-11-1-1-11000000000
χ771616160-160000-2-2-2020000000000000-4-4-40400000000000000000000000000000002220-20000000000000
χ781616-16008i2−8i200-2-2200−i2i200000000000-4-4400−2i22i20000000000000000000000000000022-200i2−i200000000000
χ791616-1600−8i28i200-2-2200i2−i200000000000-4-44002i2−2i20000000000000000000000000000022-200−i2i200000000000
χ8064-8016000-80-810-200010000000000-1620-4000200000000000000000000000000008-102000-10000000000
χ8164-80-1600080-8102000-10000000000-16204000-200000000000000000000000000008-10-200010000000000

Here i is the imaginary unit (i² = −1).