Finite Group Databasebeta

← Group #72342914

Character table — Group #72342914

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112266668888121212121212121224242424242424242424242424242424484848484848484848484848484848484848484848489696969696969696969696969696128128128128192192192192192192256256256256256256
order1244242244888822224444222244448888888822444444444488888888884444888888888836121244888861224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ31111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1
χ41111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ511-1-11-111-1-1ii−i−i1111-1-1-1-11-1-111-11-1ii−i−iii−i−i1-11-111-1-111-1-1i−iii−i−iii−i−i11-1-1i−iiiii−i−i−i−i11-1-11-1i−i1-11-1ii−i−i
χ611-1-11-111-1-1ii−i−i1111-1-1-1-11-1-111-11-1ii−i−i−i−iii-11-1111-1-1-1-111−iiii−i−i−i−iii-1-111i−i−i−i−i−iiiii11-1-1-11−ii-111-1ii−i−i
χ711-1-11-111-1-1−i−iii1111-1-1-1-11-1-111-11-1−i−iiiii−i−i-11-1111-1-1-1-111i−i−i−iiiii−i−i-1-111−iiiiii−i−i−i−i11-1-1-11i−i-111-1−i−iii
χ811-1-11-111-1-1−i−iii1111-1-1-1-11-1-111-11-1−i−iii−i−iii1-11-111-1-111-1-1−ii−i−iii−i−iii11-1-1−ii−i−i−i−iiiii11-1-11-1−ii1-11-1−i−iii
χ922222222222222222222222222222222220000000022220000002222000000002200000000-1-1-1-1000000-1-1-1-1-1-1
χ102222222222-2-2-2-22222222222222222-2-2-2-2000000002222000000-2-2-2-200000000-2-200000000-1-1-1-1000000-1-11111
χ1122-2-22-222-2-22i2i−2i−2i2222-2-2-2-22-2-222-22-22i2i−2i−2i0000000022-2-20000002i2i−2i−2i000000002i−2i00000000-1-111000000-11−i−iii
χ1222-2-22-222-2-2−2i−2i2i2i2222-2-2-2-22-2-222-22-2−2i−2i2i2i0000000022-2-2000000−2i−2i2i2i00000000−2i2i00000000-1-111000000-11ii−i−i
χ133333333333333333-1-133-1-1-1-1-13-13-1-1-1-1-1-111111111-1-1-1-11111113-13-11111-1-1-1-1-1-111-1-111-1-1000011-1-1-1-1000000
χ143333333333333333-1-133-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-13-1-1-1-1-11111-1-1-1-111-1-1110000-1-11111000000
χ1533333333333333-1-133-1-133-13-1-13-1-1-1333311111111-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1110000-1-1-1-1-1-1000000
χ1633333333333333-1-133-1-133-13-1-13-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-10000111111000000
χ1733333333333333-1-1-1-1-1-1-1-13-13-1-1-133-1-1-1-111111111-1-1-1-1111111-13-131111-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-11111000000
χ1833333333333333-1-1-1-1-1-1-1-13-13-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-13-1-1-1-11111-1-111111111000011-1-1-1-1000000
χ193333333333-3-3-3-333-1-133-1-1-1-1-13-13-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-31-31111111111111-1-111-1-10000-1-1-1-111000000
χ203333333333-3-3-3-333-1-133-1-1-1-1-13-13-1-11111-1-1-1-11111-1-1-1-11111-1-1-31-31-1-1-1-1-1-1-1-111-1-111-1-11100001111-1-1000000
χ213333333333-3-3-3-3-1-133-1-133-13-1-13-1-1-1-3-3-3-31111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-111000011-1-111000000
χ223333333333-3-3-3-3-1-133-1-133-13-1-13-1-1-1-3-3-3-3-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111111111-1-111-1-10000-1-111-1-1000000
χ233333333333-3-3-3-3-1-1-1-1-1-1-1-13-13-1-1-13311111111-1-1-1-1-1-1-1-1-1-1-1-1111-31-31111111111-1-1-1-1-1-1-1-100001111-1-1000000
χ243333333333-3-3-3-3-1-1-1-1-1-1-1-13-13-1-1-1331111-1-1-1-11111-1-1-1-11111-1-11-31-3-1-1-1-1-1-1-1-111111111110000-1-1-1-111000000
χ2533-3-33-333-3-33i3i−3i−3i33-1-1-3-311-1113-1-3-11−i−iiiii−i−i1-11-1-1-11111-1-1i−i3i−i−3iiii−i−i-1-111−iiii−i−i−i−iii00001-1−ii-11000000
χ2633-3-33-333-3-33i3i−3i−3i33-1-1-3-311-1113-1-3-11−i−iii−i−iii-11-11-1-111-1-111−ii3i−i−3ii−i−iii11-1-1−ii−i−iiiii−i−i0000-11i−i1-1000000
χ2733-3-33-333-3-33i3i−3i−3i-1-13311-3-3-1-31-131-113i3i−3i−3iii−i−i1-11-1-1-11111-1-1i−i−i−iiiii−i−i11-1-1−ii−i−iiiii−i−i0000-11−ii-11000000
χ2833-3-33-333-3-33i3i−3i−3i-1-13311-3-3-1-31-131-113i3i−3i−3i−i−iii-11-11-1-111-1-111−ii−i−iii−i−iii-1-111−iiii−i−i−i−iii00001-1i−i1-1000000
χ2933-3-33-333-3-33i3i−3i−3i-1-1-1-1111131-3-1-113-3−i−iiiii−i−i1-11-1-1-11111-1-1i−i−i3ii−3iii−i−i-1-111−ii−i−i−i−iiiii0000-11i−i1-1000000
χ3033-3-33-333-3-33i3i−3i−3i-1-1-1-1111131-3-1-113-3−i−iii−i−iii-11-11-1-111-1-111−ii−i3ii−3i−i−iii11-1-1−iiiiii−i−i−i−i00001-1−ii-11000000
χ3133-3-33-333-3-3−3i−3i3i3i33-1-1-3-311-1113-1-3-11ii−i−iii−i−i-11-11-1-111-1-111i−i−3ii3i−iii−i−i11-1-1i−iii−i−i−i−iii0000-11−ii1-1000000
χ3233-3-33-333-3-3−3i−3i3i3i33-1-1-3-311-1113-1-3-11ii−i−i−i−iii1-11-1-1-11111-1-1−ii−3ii3i−i−i−iii-1-111i−i−i−iiiii−i−i00001-1i−i-11000000
χ3333-3-33-333-3-3−3i−3i3i3i-1-13311-3-3-1-31-131-11−3i−3i3i3iii−i−i-11-11-1-111-1-111i−iii−i−iii−i−i-1-111i−i−i−iiiii−i−i00001-1−ii1-1000000
χ3433-3-33-333-3-3−3i−3i3i3i-1-13311-3-3-1-31-131-11−3i−3i3i3i−i−iii1-11-1-1-11111-1-1−iiii−i−i−i−iii11-1-1i−iii−i−i−i−iii0000-11i−i-11000000
χ3533-3-33-333-3-3−3i−3i3i3i-1-1-1-1111131-3-1-113-3ii−i−iii−i−i-11-11-1-111-1-111i−ii−3i−i3iii−i−i11-1-1i−i−i−i−i−iiiii00001-1i−i-11000000
χ3633-3-33-333-3-3−3i−3i3i3i-1-1-1-1111131-3-1-113-3ii−i−i−i−iii1-11-1-1-11111-1-1−iii−3i−i3i−i−iii-1-111i−iiiii−i−i−i−i0000-11−ii1-1000000
χ374444-4-4-44-444-44-40000000000000000000022222-2-2200002-22-2-2-200002-22-2000000000000001111000000-1-11-11-1
χ384444-4-4-44-444-44-400000000000000000000-2-2-2-2-222-20000-22-22220000-22-22000000000000001111000000-1-11-11-1
χ394444-4-4-44-44-44-44000000000000000000002222-222-20000-22-22-2-200002-22-2000000000000001111000000-1-1-11-11
χ404444-4-4-44-44-44-4400000000000000000000-2-2-2-22-2-2200002-22-2220000-22-22000000000000001111000000-1-1-11-11
χ4144-4-4-44-444-44i−4i−4i4i000000000000000000002i2i−2i−2i22-2-200002-2-22−2i2i00002i−2i−2i2i0000000000000011-1-1000000-11i−i−ii
χ4244-4-4-44-444-44i−4i−4i4i00000000000000000000−2i−2i2i2i-2-2220000-222-22i−2i0000−2i2i2i−2i0000000000000011-1-1000000-11i−i−ii
χ4344-4-4-44-444-4−4i4i4i−4i000000000000000000002i2i−2i−2i-2-2220000-222-2−2i2i00002i−2i−2i2i0000000000000011-1-1000000-11−iii−i
χ4444-4-4-44-444-4−4i4i4i−4i00000000000000000000−2i−2i2i2i22-2-200002-2-222i−2i0000−2i2i2i−2i0000000000000011-1-1000000-11−iii−i
χ4566666666666666-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000-2-2-2-20000000022000000000000000000000000
χ466666666666-6-6-6-6-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000002222000000222200000000-2-2000000000000000000000000
χ47666666-2-2-2-20000226-2226-22-2-2-2-2-2-220000222200002-22-20000220000-2-2-2-2000000002-2002-20000000000000000
χ48666666-2-2-2-20000226-2226-22-2-2-2-2-2-220000-2-2-2-200002-22-20000-2-20000222200000000-2200-220000000000000000
χ49666666-2-2-2-2000022-2622-262-2-2-2-2-2-22000022220000-22-220000220000-2-2-2-200000000-2200-220000000000000000
χ50666666-2-2-2-2000022-2622-262-2-2-2-2-2-220000-2-2-2-20000-22-220000-2-200002222000000002-2002-20000000000000000
χ51666666-2-2-2-20000-2-26-2-2-26-2-2-222-222-2000000002222-22-22-2-2-2-200000000002-22-200000000000000000000000000
χ52666666-2-2-2-20000-2-26-2-2-26-2-2-222-222-200000000-2-2-2-2-22-2222220000000000-22-2200000000000000000000000000
χ53666666-2-2-2-20000-2-2-26-2-2-26-2-222-222-20000000022222-22-2-2-2-2-20000000000-22-2200000000000000000000000000
χ54666666-2-2-2-20000-2-2-26-2-2-26-2-222-222-200000000-2-2-2-22-22-2222200000000002-22-200000000000000000000000000
χ5566-6-66-666-6-66i6i−6i−6i-2-2-2-22222-222-2-22-22−2i−2i2i2i0000000022-2-2000000−2i−2i2i2i000000002i−2i000000000000000000000000
χ5666-6-66-666-6-6−6i−6i6i6i-2-2-2-22222-222-2-22-222i2i−2i−2i0000000022-2-20000002i2i−2i−2i00000000−2i2i000000000000000000000000
χ5766-6-66-6-2-2220000226-2-2-2-62222-2-22-2-200002i2i−2i−2i00002-2-2200002i−2i0000−2i−2i2i2i000000002i−2i00−2i2i0000000000000000
χ5866-6-66-6-2-2220000226-2-2-2-62222-2-22-2-20000−2i−2i2i2i00002-2-220000−2i2i00002i2i−2i−2i00000000−2i2i002i−2i0000000000000000
χ5966-6-66-6-2-222000022-26-2-22-6222-2-22-2-200002i2i−2i−2i0000-222-200002i−2i0000−2i−2i2i2i00000000−2i2i002i−2i0000000000000000
χ6066-6-66-6-2-222000022-26-2-22-6222-2-22-2-20000−2i−2i2i2i0000-222-20000−2i2i00002i2i−2i−2i000000002i−2i00−2i2i0000000000000000
χ6166-6-66-6-2-2220000-2-26-222-62-22-22-2-222000000002-22-2-222-2-2-22200000000002-2-2200000000000000000000000000
χ6266-6-66-6-2-2220000-2-26-222-62-22-22-2-22200000000-22-22-222-222-2-20000000000-222-200000000000000000000000000
χ6366-6-66-6-2-2220000-2-2-26222-6-22-22-2-222000000002-22-22-2-22-2-2220000000000-222-200000000000000000000000000
χ6466-6-66-6-2-2220000-2-2-26222-6-22-22-2-22200000000-22-222-2-2222-2-200000000002-2-2200000000000000000000000000
χ658888-8-8-88-888-88-8000000000000000000000000000000000000000000000000000000000000-1-1-1-100000011-11-11
χ668888-8-8-88-88-88-88000000000000000000000000000000000000000000000000000000000000-1-1-1-1000000111-11-1
χ6788-8-8-88-888-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000-1-1110000001-1−iii−i
χ6888-8-8-88-888-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000-1-1110000001-1i−i−ii
χ698-88i−8i00000000004-4004i−4i000000000000004ζ−4ζ4ζ3−4ζ300000000000000000000000000002ζ−2ζ002ζ3−2ζ3002-22i−2i000000000000
χ708-88i−8i00000000004-4004i−4i00000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000−2ζ2ζ00−2ζ32ζ3002-22i−2i000000000000
χ718-8−8i8i00000000004-400−4i4i000000000000004ζ3−4ζ34ζ−4ζ00000000000000000000000000002ζ3−2ζ3002ζ−2ζ002-2−2i2i000000000000
χ728-8−8i8i00000000004-400−4i4i00000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000−2ζ32ζ300−2ζ2ζ002-2−2i2i000000000000
χ73121212121212-4-4-4-4000044-4-444-4-4-444-44-44-4000000000000000000000000000000000000000000000000000000000000
χ74121212121212-4-4-4-40000-4-4-4-4-4-4-4-444-4444-44000000000000000000000000000000000000000000000000000000000000
χ7512121212-12-124-44-4000000000000000000004-4-4422222-2-220000-22-22-2-20000-22-22000000000000000000000000000000
χ7612121212-12-124-44-4000000000000000000004-4-44-2-2-2-2-222-200002-22-22200002-22-2000000000000000000000000000000
χ7712121212-12-124-44-400000000000000000000-444-42222-222-200002-22-2-2-20000-22-22000000000000000000000000000000
χ7812121212-12-124-44-400000000000000000000-444-4-2-2-2-22-2-220000-22-222200002-22-2000000000000000000000000000000
χ791212-12-1212-12-4-444000044-4-4-4-444-4-4-4-44444000000000000000000000000000000000000000000000000000000000000
χ801212-12-1212-12-4-4440000-4-4-4-444444-4444-4-4-4000000000000000000000000000000000000000000000000000000000000
χ811212-12-12-12124-4-44000000000000000000004i−4i4i−4i2i2i−2i−2i22-2-20000-222-2−2i2i0000−2i2i2i−2i000000000000000000000000000000
χ821212-12-12-12124-4-44000000000000000000004i−4i4i−4i−2i−2i2i2i-2-22200002-2-222i−2i00002i−2i−2i2i000000000000000000000000000000
χ831212-12-12-12124-4-4400000000000000000000−4i4i−4i4i2i2i−2i−2i-2-22200002-2-22−2i2i0000−2i2i2i−2i000000000000000000000000000000
χ841212-12-12-12124-4-4400000000000000000000−4i4i−4i4i−2i−2i2i2i22-2-20000-222-22i−2i00002i−2i−2i2i000000000000000000000000000000
χ8516-1616i−16i00000000008-8008i−8i000000000000000000000000000000000000000000000000000000-22−2i2i000000000000
χ8616-16−16i16i00000000008-800−8i8i000000000000000000000000000000000000000000000000000000-222i−2i000000000000
χ8724-2424i−24i0000000000-4400−4i4i000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000−2ζ2ζ00−2ζ32ζ3000000000000000000
χ8824-2424i−24i0000000000-4400−4i4i00000000000000−4ζ4ζ−4ζ34ζ300000000000000000000000000002ζ−2ζ002ζ3−2ζ3000000000000000000
χ8924-24−24i24i0000000000-44004i−4i000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000−2ζ32ζ300−2ζ2ζ000000000000000000
χ9024-24−24i24i0000000000-44004i−4i00000000000000−4ζ34ζ3−4ζ4ζ00000000000000000000000000002ζ3−2ζ3002ζ−2ζ000000000000000000

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