Finite Group Databasebeta

← Group #72324302

Character table — Group #72324302

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11222444444448888888888816161616161616161616161616161616161616161616161616161616323232323232646464646464646464646464128128128128
order12222222244442222244444422222224444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111-1-11111-1-111-11111111-111111111111111111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−i
χ61111111111111111-1-11111-1-111-11111111-111111111111111111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii
χ71111111111111111-1-11111-1-111-1-1-1-1-1111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−i−ii
χ81111111111111111-1-11111-1-111-1-1-1-1-1111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−iii−i
χ91111111111111-1-111111-1-1111-1111-1-11-1-1111-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ101111111111111-1-111111-1-1111-1111-1-11-1-1111-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ111111111111111-1-111111-1-1111-11-1-1111-1-11-1-11111-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-111
χ121111111111111-1-111111-1-1111-11-1-1111-1-11-1-11111-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1111111-1-1
χ131111111111111-1-11-1-111-1-1-1-11-1-111-1-11-1-1-111-1-111-1-1-11111-1-1-1-11111-1-1-1-111ii−i−iii−i−i−ii−ii
χ141111111111111-1-11-1-111-1-1-1-11-1-111-1-11-1-1-111-1-111-1-1-11111-1-1-1-11111-1-1-1-111−i−iii−i−iiii−ii−i
χ151111111111111-1-11-1-111-1-1-1-11-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-1-111111111-1-111-1-1ii−i−i−i−iii−iii−i
χ161111111111111-1-11-1-111-1-1-1-11-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-1-111111111-1-111-1-1−i−iiiii−i−ii−i−ii
χ17222222222222200222220022-2022-200-20022-200-2-200022-2-200000000-2-22-200000000000000
χ18222222222222200222220022-202-2200-2002-2200-2-2000-2-22200000000-2-2-2200000000000000
χ192222222222222002-2-22200-2-2-20-22-200-200-22-200-2-200022-2-20000000022-2200000000000000
χ202222222222222002-2-22200-2-2-20-2-2200-200-2-2200-2-2000-2-22200000000222-200000000000000
χ21222222222-2-2-2-200222-2-200-2-2-202002-2-200-2002-222000000022-2-200002-2002-2000000000000
χ22222222222-2-2-2-200222-2-200-2-2-20200-22-200-200-22220000000-2-22200002-200-22000000000000
χ23222222222-2-2-2-2002-2-2-2-20022-20-2002-2-2002002-222000000022-2-20000-2200-22000000000000
χ24222222222-2-2-2-2002-2-2-2-20022-20-200-22-200200-22220000000-2-2220000-22002-2000000000000
χ25222222222-2-2-2-222222-2-2-2-2-2-222200002-2-2-20000-2-222-20000000022-2-2-220000000000000000
χ26222222222-2-2-2-2222-2-2-2-2-2-22222-200002-2-220000-2-222-200000000-2-2222-20000000000000000
χ27222222222-2-2-2-2-2-2222-2-222-2-22-220000222-20000-2-2-2-2200000000-2-222-220000000000000000
χ28222222222-2-2-2-2-2-22-2-2-2-222222-2-2000022220000-2-2-2-220000000022-2-22-20000000000000000
χ294444444-4-4000000-400004400-40000004-4-40000000004000000000000000000000000000000
χ304444444-4-4000000-40000-4-400-4000000444000000000-4000000000000000000000000000000
χ314444444-4-4000044-4000000004400000-4000000000-4-40000000000000000000000000000000
χ324444444-4-40000-4-4-4000000004-400000-4000000000440000000000000000000000000000000
χ3344444-4-44444-4-400-4004-400000000400000004000000000-4-400000000000000000000000000
χ3444444-4-44444-4-400-4004-400000000-40000000-40000000004400000000000000000000000000
χ3544444-4-444-4-44400-400-44000000040000000400000000-4-40000000000000000000000000000
χ3644444-4-444-4-44400-400-440000000-40000000-400000000440000000000000000000000000000
χ3744444-4-4-4-40000004000000000000004000000044-4000000000-4-40000000000000000000000
χ3844444-4-4-4-4000000400000000000000-40000000-44-4000000000440000000000000000000000
χ3944444-4-4-4-4000000400000000000004000000040-440000000-4-4000000000000000000000000
χ4044444-4-4-4-400000040000000000000-40000000-40-44000000044000000000000000000000000
χ4144-4-44004-40044220000-422000-20002-202-2000-22002-2-24-4002-22-20000000000000000000000
χ4244-4-44004-40044220000-422000-2000-2202-20002-2002-2-2-4400-22-220000000000000000000000
χ4344-4-44004-40044-2-20000-4-2-200020002-20-22000-2200-222-44002-22-20000000000000000000000
χ4444-4-44004-40044-2-20000-4-2-20002000-220-220002-200-2224-400-22-220000000000000000000000
χ4544-4-44004-400-4-42200004-2-2000-2040220-220-40-2-2002-2200002-2-220000000000000000000000
χ4644-4-44004-400-4-42200004-2-2000-20-40-2-20-2204022002-220000-222-20000000000000000000000
χ4744-4-44004-400-4-4-2-200004220002040-2-202-20-402200-22-20000-222-20000000000000000000000
χ4844-4-44004-400-4-4-2-2000042200020-402202-2040-2-200-22-200002-2-220000000000000000000000
χ4944-4-4400-44440022000-4022000-20002-20-22000-2200-22-2004-4-22-220000000000000000000000
χ5044-4-4400-44440022000-4022000-2000-220-220002-200-22-200-442-22-20000000000000000000000
χ5144-4-4400-444400-2-2000-40-2-200020002-202-2000-22002-2200-44-22-220000000000000000000000
χ5244-4-4400-444400-2-2000-40-2-20002000-2202-20002-2002-22004-42-22-20000000000000000000000
χ5344-4-4400-44-4-4002200040-2-2000-20042202-200-4-2-200-2220000-222-20000000000000000000000
χ5444-4-4400-44-4-4002200040-2-2000-200-4-2-202-20042200-22200002-2-220000000000000000000000
χ5544-4-4400-44-4-400-2-200040220002004-2-20-2200-422002-2-200002-2-220000000000000000000000
χ5644-4-4400-44-4-400-2-20004022000200-4220-22004-2-2002-2-20000-222-20000000000000000000000
χ57888-8-800000000000000000440000000000-400000000000000000000000000000002-22-20000
χ58888-8-800000000000000000440000000000-40000000000000000000000000000000-22-220000
χ59888-8-800000000000000000-4-40000000000400000000000000000000000000000002i−2i−2i2i0000
χ60888-8-800000000000000000-4-4000000000040000000000000000000000000000000−2i2i2i−2i0000
χ6188-88-8000000000004400000000-4000000000000000000000000000000000002-22-200000000
χ6288-88-8000000000004400000000-400000000000000000000000000000000000-22-2200000000
χ6388-88-800000000000-4-4000000004000000000000000000000000000000000002i−2i−2i2i00000000
χ6488-88-800000000000-4-400000000400000000000000000000000000000000000−2i2i2i−2i00000000
χ658-80004-4004i−4i4i−4i4-404-4004i−4i4i−4i00000000000000000000000000002-22i−2i000000000000000000
χ668-80004-4004i−4i4i−4i4-40-44004i−4i−4i4i0000000000000000000000000000-22−2i2i000000000000000000
χ678-80004-4004i−4i4i−4i-4404-400−4i4i4i−4i0000000000000000000000000000-22−2i2i000000000000000000
χ688-80004-4004i−4i4i−4i-440-4400−4i4i−4i4i00000000000000000000000000002-22i−2i000000000000000000
χ698-80004-400−4i4i−4i4i4-404-400−4i4i−4i4i00000000000000000000000000002-2−2i2i000000000000000000
χ708-80004-400−4i4i−4i4i4-40-4400−4i4i4i−4i0000000000000000000000000000-222i−2i000000000000000000
χ718-80004-400−4i4i−4i4i-4404-4004i−4i−4i4i0000000000000000000000000000-222i−2i000000000000000000
χ728-80004-400−4i4i−4i4i-440-44004i−4i4i−4i00000000000000000000000000002-2−2i2i000000000000000000
χ7316-16000-88008i−8i−8i8i0000000000000000000000000000000000000000000000000000000000000
χ7416-16000-8800−8i8i8i−8i0000000000000000000000000000000000000000000000000000000000000

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