Finite Group Databasebeta

← Group #72342913

Character table — Group #72342913

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112266668888121212121212121224242424242424242424242424242424484848484848484848484848484848484848484848489696969696969696969696969696128128128128192192192192192192256256256256256256
order12442422442244222244442222224444448888444444448888888888888844888888888888361212448888666121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ31111111111-1-1-1-111111111111-1-1111-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-11-1-11-1-1
χ41111111111-1-1-1-111111111111-1-1111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1-11-1-1
χ511-1-11-111-1-11-11-11111-1-1-1-111-11-1-1111-1-1-1ii−i−i11-1-111-1-1i−iii−i−iii−i−iii−i−i1-1ii−i−iii−i−iii−i−i11-1-1i−ii−ii−i11-1-11-1
χ611-1-11-111-1-11-11-11111-1-1-1-111-11-1-1111-1-1-1−i−iii11-1-111-1-1−ii−i−iii−i−iii−i−iii1-1−i−iii−i−iii−i−iii11-1-1−ii−ii−ii11-1-11-1
χ711-1-11-111-1-1-11-111111-1-1-1-111-1-11-111-11-1-1ii−i−i11-1-1-1-111i−i−i−iiiii−i−i−i−iii-11ii−i−iii−i−i−i−iii11-1-1−iii−i−ii1-11-1-11
χ811-1-11-111-1-1-11-111111-1-1-1-111-1-11-111-11-1-1−i−iii11-1-1-1-111−iiii−i−i−i−iiiii−i−i-11−i−iii−i−iiiii−i−i11-1-1i−i−iii−i1-11-1-11
χ922222222222222222222222222222222220000222222220000000000000022000000000000-1-1-1-1000000-1-1-1-1-1-1
χ102222222222-2-2-2-222222222222-2-2222-2-22200002222-2-2-2-200000000000000-2-2000000000000-1-1-1-1000000-111-111
χ1122-2-22-222-2-22-22-22222-2-2-2-222-22-2-2222-2-2-2000022-2-222-2-2000000000000002-2000000000000-1-111000000-1-111-11
χ1222-2-22-222-2-2-22-222222-2-2-2-222-2-22-222-22-2-2000022-2-2-2-22200000000000000-22000000000000-1-111000000-11-111-1
χ133333333333333333-1-133-1-13-1-1-1-1-1-1-1-1-13-11111-1-1-1-13-13-111111111111111-1-11111-1-1-1-1-1-1-1-10000-1-1-1-111000000
χ143333333333333333-1-133-1-13-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111100001111-1-1000000
χ1533333333333333-1-133-1-133-1-1333-13-133-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111110000-1-1-1-1-1-1000000
χ1633333333333333-1-133-1-133-1-1333-13-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-10000111111000000
χ1733333333333333-1-1-1-1-1-1-1-1-13-1-1-13-13-1-1-131111-1-1-1-1-13-1311111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111-1-1000000
χ1833333333333333-1-1-1-1-1-1-1-1-13-1-1-13-13-1-1-13-1-1-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111110000-1-1-1-111000000
χ193333333333-3-3-3-333-1-133-1-13-1-111-1-1-1113-11111-1-1-1-1-31-3111-1-1-1-11111-1-1-1-1111111-1-1-1-11111000011-1-1-1-1000000
χ203333333333-3-3-3-333-1-133-1-13-1-111-1-1-1113-1-1-1-1-1-1-1-1-1-31-31-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-10000-1-11111000000
χ213333333333-3-3-3-3-1-133-1-133-1-13-3-3-13-1-3-3-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1000011-1-111000000
χ223333333333-3-3-3-3-1-133-1-133-1-13-3-3-13-1-3-3-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111111111-1-1-1-111110000-1-111-1-1000000
χ233333333333-3-3-3-3-1-1-1-1-1-1-1-1-13-1113-1311-131111-1-1-1-11-31-311-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111110000-1-11111000000
χ243333333333-3-3-3-3-1-1-1-1-1-1-1-1-13-1113-1311-13-1-1-1-1-1-1-1-11-31-3-1-11111-1-1-1-111111111111111-1-1-1-1000011-1-1-1-1000000
χ2533-3-33-333-3-33-33-333-1-1-3-3113-11-111-1-1-11-31ii−i−i-1-1113-1-31i−iii−i−iii−i−iii−i−i-11ii−i−i−i−iii−i−iii0000−ii−iii−i000000
χ2633-3-33-333-3-33-33-333-1-1-3-3113-11-111-1-1-11-31−i−iii-1-1113-1-31−ii−i−iii−i−iii−i−iii-11−i−iiiii−i−iii−i−i0000i−ii−i−ii000000
χ2733-3-33-333-3-33-33-3-1-13311-3-3-1-1-33-313-13-311ii−i−i-1-111-1-111i−iii−i−iii−i−iii−i−i-11−i−iiiii−i−iii−i−i0000−ii−ii−ii000000
χ2833-3-33-333-3-33-33-3-1-13311-3-3-1-1-33-313-13-311−i−iii-1-111-1-111−ii−i−iii−i−iii−i−iii-11ii−i−i−i−iii−i−iii0000i−ii−ii−i000000
χ2933-3-33-333-3-33-33-3-1-1-1-11111-131-11-3-13-111-3ii−i−i-1-111-131-3i−iii−i−iii−i−iii−i−i-11−i−iii−i−iii−i−iii0000i−ii−i−ii000000
χ3033-3-33-333-3-33-33-3-1-1-1-11111-131-11-3-13-111-3−i−iii-1-111-131-3−ii−i−iii−i−iii−i−iii-11ii−i−iii−i−iii−i−i0000−ii−iii−i000000
χ3133-3-33-333-3-3-33-3333-1-1-3-3113-111-11-1-11-1-31ii−i−i-1-111-313-1i−i−i−iiiii−i−i−i−iii1-1ii−i−i−i−iiiii−i−i0000i−i−ii−ii000000
χ3233-3-33-333-3-3-33-3333-1-1-3-3113-111-11-1-11-1-31−i−iii-1-111-313-1−iiii−i−i−i−iiiii−i−i1-1−i−iiiii−i−i−i−iii0000−iii−ii−i000000
χ3333-3-33-333-3-3-33-33-1-13311-3-3-1-1-3-3313-1-3311ii−i−i-1-11111-1-1i−i−i−iiiii−i−i−i−iii1-1−i−iiiii−i−i−i−iii0000i−i−iii−i000000
χ3433-3-33-333-3-3-33-33-1-13311-3-3-1-1-3-3313-1-3311−i−iii-1-11111-1-1−iiii−i−i−i−iiiii−i−i1-1ii−i−i−i−iiiii−i−i0000−iii−i−ii000000
χ3533-3-33-333-3-3-33-33-1-1-1-11111-1311-1-3-131-11-3ii−i−i-1-1111-3-13i−i−i−iiiii−i−i−i−iii1-1−i−iii−i−iiiii−i−i0000−iii−ii−i000000
χ3633-3-33-333-3-3-33-33-1-1-1-11111-1311-1-3-131-11-3−i−iii-1-1111-3-13−iiii−i−i−i−iiiii−i−i1-1ii−i−iii−i−i−i−iii0000i−i−ii−ii000000
χ374444-4-44-4-444-4-4400000000000000000000222200000000-2-22-22-22-22-22-22-2000000000000001111000000-11-1-1-11
χ384444-4-44-4-444-4-4400000000000000000000-2-2-2-20000000022-22-22-22-22-22-22000000000000001111000000-11-1-1-11
χ394444-4-44-4-44-444-400000000000000000000222200000000-2-2-22-222-22-2-22-22000000000000001111000000-1-11-11-1
χ404444-4-44-4-44-444-400000000000000000000-2-2-2-200000000222-22-2-22-222-22-2000000000000001111000000-1-11-11-1
χ4144-4-4-444-44-444-4-4000000000000000000002i2i−2i−2i00000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000011-1-1000000-1111-1-1
χ4244-4-4-444-44-444-4-400000000000000000000−2i−2i2i2i000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000011-1-1000000-1111-1-1
χ4344-4-4-444-44-4-4-444000000000000000000002i2i−2i−2i00000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000011-1-1000000-1-1-1111
χ4444-4-4-444-44-4-4-44400000000000000000000−2i−2i2i2i000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000011-1-1000000-1-1-1111
χ4566666666666666-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200002222-2-2-2-200000000000000220000000000000000000000000000
χ466666666666-6-6-6-6-2-2-2-2-2-2-2-2-2-2-222-2-2-222-2-200002222222200000000000000-2-20000000000000000000000000000
χ47666666-2-2-2-20000226-2226-2-22-200-2-2-200-2222222-22-20000220000-2-2-2-200000000002-22-200000000000000000000
χ48666666-2-2-2-20000226-2226-2-22-200-2-2-200-22-2-2-2-22-22-20000-2-2000022220000000000-22-2200000000000000000000
χ49666666-2-2-2-2000022-2622-26-22-200-2-2-200-222222-22-220000220000-2-2-2-20000000000-22-2200000000000000000000
χ50666666-2-2-2-2000022-2622-26-22-200-2-2-200-22-2-2-2-2-22-220000-2-20000222200000000002-22-200000000000000000000
χ51666666-2-2-2-20000-2-26-2-2-26-22-2-2002-22002-20000-22-2200000022220000-2-2-2-200000000002-22-20000000000000000
χ52666666-2-2-2-20000-2-26-2-2-26-22-2-2002-22002-20000-22-22000000-2-2-2-2000022220000000000-22-220000000000000000
χ53666666-2-2-2-20000-2-2-26-2-2-262-2-2002-22002-200002-22-200000022220000-2-2-2-20000000000-22-220000000000000000
χ54666666-2-2-2-20000-2-2-26-2-2-262-2-2002-22002-200002-22-2000000-2-2-2-20000222200000000002-22-20000000000000000
χ5566-6-66-666-6-66-66-6-2-2-2-22222-2-22-222-2-2-2222000022-2-2-2-222000000000000002-20000000000000000000000000000
χ5666-6-66-666-6-6-66-66-2-2-2-22222-2-222-22-2-22-222000022-2-222-2-200000000000000-220000000000000000000000000000
χ5766-6-66-6-2-2220000226-2-2-2-62-222002-2-2002-22i2i−2i−2i2-2-2200002i−2i0000−2i−2i2i2i00000000002i−2i−2i2i00000000000000000000
χ5866-6-66-6-2-2220000226-2-2-2-62-222002-2-2002-2−2i−2i2i2i2-2-220000−2i2i00002i2i−2i−2i0000000000−2i2i2i−2i00000000000000000000
χ5966-6-66-6-2-222000022-26-2-22-6-222002-2-2002-22i2i−2i−2i-222-200002i−2i0000−2i−2i2i2i0000000000−2i2i2i−2i00000000000000000000
χ6066-6-66-6-2-222000022-26-2-22-6-222002-2-2002-2−2i−2i2i2i-222-20000−2i2i00002i2i−2i−2i00000000002i−2i−2i2i00000000000000000000
χ6166-6-66-6-2-2220000-2-26-222-622-2200-2-2200-220000-222-20000002i2i−2i−2i0000−2i−2i2i2i00000000002i−2i−2i2i0000000000000000
χ6266-6-66-6-2-2220000-2-26-222-622-2200-2-2200-220000-222-2000000−2i−2i2i2i00002i2i−2i−2i0000000000−2i2i2i−2i0000000000000000
χ6366-6-66-6-2-2220000-2-2-26222-62-2200-2-2200-2200002-2-220000002i2i−2i−2i0000−2i−2i2i2i0000000000−2i2i2i−2i0000000000000000
χ6466-6-66-6-2-2220000-2-2-26222-62-2200-2-2200-2200002-2-22000000−2i−2i2i2i00002i2i−2i−2i00000000002i−2i−2i2i0000000000000000
χ658888-8-88-8-888-8-88000000000000000000000000000000000000000000000000000000000000-1-1-1-10000001-1111-1
χ668888-8-88-8-88-888-8000000000000000000000000000000000000000000000000000000000000-1-1-1-100000011-11-11
χ6788-8-8-888-88-888-8-8000000000000000000000000000000000000000000000000000000000000-1-1110000001-1-1-111
χ6888-8-8-888-88-8-8-888000000000000000000000000000000000000000000000000000000000000-1-111000000111-1-1-1
χ698-88i−8i00000000004-4004i−4i000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000002ζ−2ζ2ζ3−2ζ3000000002-22i−2i000000000000
χ708-88i−8i00000000004-4004i−4i00000000000000−4ζ4ζ−4ζ34ζ3000000000000000000000000−2ζ2ζ−2ζ32ζ3000000002-22i−2i000000000000
χ718-8−8i8i00000000004-400−4i4i000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000002ζ3−2ζ32ζ−2ζ000000002-2−2i2i000000000000
χ728-8−8i8i00000000004-400−4i4i00000000000000−4ζ34ζ3−4ζ4ζ000000000000000000000000−2ζ32ζ3−2ζ2ζ000000002-2−2i2i000000000000
χ73121212121212-4-4-4-4000044-4-444-4-4-4-440044400-4-400000000000000000000000000000000000000000000000000000000
χ74121212121212-4-4-4-40000-4-4-4-4-4-4-4-444400-44-4004400000000000000000000000000000000000000000000000000000000
χ7512121212-12-12-444-40000000000000004-4000-4400222200000000-2-22-22-2-22-22-22-22000000000000000000000000000000
χ7612121212-12-12-444-40000000000000004-4000-4400-2-2-2-20000000022-22-222-22-22-22-2000000000000000000000000000000
χ7712121212-12-12-444-4000000000000000-440004-400222200000000-2-2-22-22-22-222-22-2000000000000000000000000000000
χ7812121212-12-12-444-4000000000000000-440004-400-2-2-2-200000000222-22-22-22-2-22-22000000000000000000000000000000
χ791212-12-1212-12-4-444000044-4-4-4-444-4-4-400-444004400000000000000000000000000000000000000000000000000000000
χ801212-12-1212-12-4-4440000-4-4-4-4444444-40044-400-4-400000000000000000000000000000000000000000000000000000000
χ811212-12-12-1212-44-4400000000000000044000-4-4002i2i−2i−2i00000000−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ821212-12-12-1212-44-4400000000000000044000-4-400−2i−2i2i2i000000002i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ831212-12-12-1212-44-44000000000000000-4-400044002i2i−2i−2i00000000−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ841212-12-12-1212-44-44000000000000000-4-40004400−2i−2i2i2i000000002i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ8516-1616i−16i00000000008-8008i−8i000000000000000000000000000000000000000000000000000000-22−2i2i000000000000
χ8616-16−16i16i00000000008-800−8i8i000000000000000000000000000000000000000000000000000000-222i−2i000000000000
χ8724-2424i−24i0000000000-4400−4i4i000000000000004ζ−4ζ4ζ3−4ζ3000000000000000000000000−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ8824-2424i−24i0000000000-4400−4i4i00000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ8924-24−24i24i0000000000-44004i−4i000000000000004ζ3−4ζ34ζ−4ζ000000000000000000000000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ9024-24−24i24i0000000000-44004i−4i00000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000002ζ3−2ζ32ζ−2ζ000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.