Finite Group Databasebeta

← Group #72317472

Character table — Group #72317472

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111222222444444444444444488888888888888161616161616161616161616161616161616161632323232323232323232323232323232
order1244222444222222224444444422244488888888224444448888888888884444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911-1-1111-1-1-1111111-1-111-1-1-1-1-1-111-1-1-11iiii−i−i−i−i1-11-111-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−iii−i−i11-1-1
χ1011-1-1111-1-1-1111111-1-111-1-1-1-1-1-111-1-1-11iiii−i−i−i−i1-11-111-1-1−i−iiiii−i−i−i−iii-1-111−i−iiiii−i−i-1-111
χ1111-1-1111-1-1-1111111-1-111-1-1-1-1-1-111-1-1-11iiii−i−i−i−i-11-11-1-111ii−i−iii−i−iii−i−i11-1-1−i−iii−i−iii-1-111
χ1211-1-1111-1-1-1111111-1-111-1-1-1-1-1-111-1-1-11iiii−i−i−i−i-11-11-1-111−i−iiiii−i−i−i−iii-1-111ii−i−i−i−iii11-1-1
χ1311-1-1111-1-1-1111111-1-111-1-1-1-1-1-111-1-1-11−i−i−i−iiiii1-11-111-1-1ii−i−i−i−iiiii−i−i-1-111ii−i−i−i−iii-1-111
χ1411-1-1111-1-1-1111111-1-111-1-1-1-1-1-111-1-1-11−i−i−i−iiiii1-11-111-1-1−i−iii−i−iii−i−iii11-1-1−i−iii−i−iii11-1-1
χ1511-1-1111-1-1-1111111-1-111-1-1-1-1-1-111-1-1-11−i−i−i−iiiii-11-11-1-111ii−i−i−i−iiiii−i−i-1-111−i−iiiii−i−i11-1-1
χ1611-1-1111-1-1-1111111-1-111-1-1-1-1-1-111-1-1-11−i−i−i−iiiii-11-11-1-111−i−iii−i−iii−i−iii11-1-1ii−i−iii−i−i-1-111
χ172222222222222222-2-2-2-2222222-2-2-2-2-2-222222222000000000000-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000222200000000000000000000
χ19222222222222-2-2-2-2222222-2-2-2-2-2-22-2-22000000000000000000000000000000002-22-200000000
χ20222222222222-2-2-2-2222222-2-2-2-2-2-22-2-2200000000000000000000000000000000-22-2200000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-222-222-200000000000000000000000000000000000000002i−2i2i−2i
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-222-222-20000000000000000000000000000000000000000−2i2i−2i2i
χ232222222222-2-222-2-22222-2-2-2-2222-2-22-2-2000000002222-2-2-2-20000000000000000000000000000
χ242222222222-2-222-2-22222-2-2-2-2222-2-22-2-200000000-2-2-2-222220000000000000000000000000000
χ252222222222-2-222-2-2-2-2-2-2-2-2-2-222-222-2220000000000000000000000000000000000002-22-20000
χ262222222222-2-222-2-2-2-2-2-2-2-2-2-222-222-222000000000000000000000000000000000000-22-220000
χ272222222222-2-2-2-2222222-2-222-2-2-22-2-22-2000000000000000022220000-2-2-2-20000000000000000
χ282222222222-2-2-2-2222222-2-222-2-2-22-2-22-20000000000000000-2-2-2-2000022220000000000000000
χ292222222222-2-2-2-222-2-2-2-2-2-222-2-22-222-2200000000000000000000000000002-22-2000000000000
χ302222222222-2-2-2-222-2-2-2-2-2-222-2-22-222-220000000000000000000000000000-22-22000000000000
χ3122-2-2222-2-2-222222222-2-2-2-2-2-2-2-2-2-2222-22i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i00000000000000000000
χ3222-2-2222-2-2-222222222-2-2-2-2-2-2-2-2-2-2222-2−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i00000000000000000000
χ3322-2-2222-2-2-222-2-2-2-222-2-2-2-22222222-2-2-200000000000000000000000000000000000000002i−2i−2i2i
χ3422-2-2222-2-2-222-2-2-2-222-2-2-2-22222222-2-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ3522-2-2222-2-2-222-2-2-2-2-2-222-2-22222-2-2-2222000000000000000000000000000000002i−2i−2i2i00000000
χ3622-2-2222-2-2-222-2-2-2-2-2-222-2-22222-2-2-222200000000000000000000000000000000−2i2i2i−2i00000000
χ3722-2-2222-2-2-2-2-222-2-222-2-22222-2-2-22-22-220000000000000000000000000000000000002i−2i−2i2i0000
χ3822-2-2222-2-2-2-2-222-2-222-2-22222-2-2-22-22-22000000000000000000000000000000000000−2i2i2i−2i0000
χ3922-2-2222-2-2-2-2-222-2-2-2-2222222-2-22-22-22-2000000002-22-2-2-2220000000000000000000000000000
χ4022-2-2222-2-2-2-2-222-2-2-2-2222222-2-22-22-22-200000000-22-2222-2-20000000000000000000000000000
χ4122-2-2222-2-2-2-2-2-2-22222-2-222-2-2222-2-2-22200000000000000000000000000002-2-22000000000000
χ4222-2-2222-2-2-2-2-2-2-22222-2-222-2-2222-2-2-2220000000000000000000000000000-222-2000000000000
χ4322-2-2222-2-2-2-2-2-2-222-2-22222-2-222-2222-2-200000000000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ4422-2-2222-2-2-2-2-2-2-222-2-22222-2-222-2222-2-20000000000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ4544444-4-4-44-40000004-44-400000000000022-2-222-2-20000000000002-22-200000000000000000000
χ4644444-4-4-44-40000004-44-4000000000000-2-222-2-222000000000000-22-2200000000000000000000
χ4744444-4-4-44-4000000-44-4400000000000022-2-222-2-2000000000000-22-2200000000000000000000
χ4844444-4-4-44-4000000-44-44000000000000-2-222-2-2220000000000002-22-200000000000000000000
χ494444-44-4-4-44004-400000000004-400000000000000000000002-22-200002-22-20000000000000000
χ504444-44-4-4-44004-400000000004-40000000000000000000000-22-220000-22-220000000000000000
χ514444-44-4-4-4400-440000000000-4400000000000000000000002-22-20000-22-220000000000000000
χ524444-44-4-4-4400-440000000000-440000000000000000000000-22-2200002-22-20000000000000000
χ534444-4-444-4-400004-40000004-400000000000000002-2-222-22-20000000000000000000000000000
χ544444-4-444-4-400004-40000004-40000000000000000-222-2-22-220000000000000000000000000000
χ554444-4-444-4-40000-44000000-4400000000000000002-2-22-22-220000000000000000000000000000
χ564444-4-444-4-40000-44000000-440000000000000000-222-22-22-20000000000000000000000000000
χ5744-4-44-4-44-440000004-4-440000000000002i2i−2i−2i−2i−2i2i2i000000000000−2i2i2i−2i00000000000000000000
χ5844-4-44-4-44-440000004-4-44000000000000−2i−2i2i2i2i2i−2i−2i0000000000002i−2i−2i2i00000000000000000000
χ5944-4-44-4-44-44000000-444-40000000000002i2i−2i−2i−2i−2i2i2i0000000000002i−2i−2i2i00000000000000000000
χ6044-4-44-4-44-44000000-444-4000000000000−2i−2i2i2i2i2i−2i−2i000000000000−2i2i2i−2i00000000000000000000
χ6144-4-4-44-444-4004-40000000000-4400000000000000000000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ6244-4-4-44-444-4004-40000000000-440000000000000000000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ6344-4-4-44-444-400-4400000000004-400000000000000000000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ6444-4-4-44-444-400-4400000000004-40000000000000000000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ6544-4-4-4-44-44400004-4000000-44000000000000000022-2-22-2-220000000000000000000000000000
χ6644-4-4-4-44-44400004-4000000-440000000000000000-2-222-222-20000000000000000000000000000
χ6744-4-4-4-44-4440000-440000004-4000000000000000022-2-2-222-20000000000000000000000000000
χ6844-4-4-4-44-4440000-440000004-40000000000000000-2-2222-2-220000000000000000000000000000
χ698-88i−8i0000004-4000000004i−4i0000000000004ζ−4ζ004ζ3−4ζ3000000000000000000000000000000000000
χ708-88i−8i0000004-4000000004i−4i000000000000−4ζ4ζ00−4ζ34ζ3000000000000000000000000000000000000
χ718-88i−8i000000-4400000000−4i4i00000000004ζ−4ζ004ζ3−4ζ300000000000000000000000000000000000000
χ728-88i−8i000000-4400000000−4i4i0000000000−4ζ4ζ00−4ζ34ζ300000000000000000000000000000000000000
χ738-8−8i8i0000004-400000000−4i4i0000000000004ζ3−4ζ3004ζ−4ζ000000000000000000000000000000000000
χ748-8−8i8i0000004-400000000−4i4i000000000000−4ζ34ζ300−4ζ4ζ000000000000000000000000000000000000
χ758-8−8i8i000000-44000000004i−4i00000000004ζ3−4ζ3004ζ−4ζ00000000000000000000000000000000000000
χ768-8−8i8i000000-44000000004i−4i0000000000−4ζ34ζ300−4ζ4ζ00000000000000000000000000000000000000

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