Finite Group Databasebeta

← Group #72317706

Character table — Group #72317706

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122222244444444444444448888881616161616161616161616161616161616161616161616161616161616161616323232323232323232323232
order1244222444222222224444444422244488888888888888888888888888888888444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iii−i−iii−i−iii−i−i
χ101111111111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−iii−i−iii−i−iii
χ111111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−i−i−iii−i−iii
χ121111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iiiii−i−iii−i−i
χ131111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111iiii−i−i−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−i−i−iiiiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-22222-2-2-2-2222-2-2-2-220000000022-2-20000000022-2-200000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-2222-2-2-2-2200000000-2-22200000000-2-22200000000000000000000
χ19222222222222-2-2-2-2-2-222-2-2-2-2-2-2-22222-20000000022-2-200000000-2-22200000000000000000000
χ20222222222222-2-2-2-2-2-222-2-2-2-2-2-2-22222-200000000-2-2220000000022-2-200000000000000000000
χ212222222222-2-222-2-222-2-222-2-222-22-22-2-2000022-2-20000000022-2-2000000000000000000000000
χ222222222222-2-222-2-222-2-222-2-222-22-22-2-20000-2-22200000000-2-222000000000000000000000000
χ232222222222-2-222-2-2-2-2-2-222-2-2-2-22-22-222000022-2-200000000-2-222000000000000000000000000
χ242222222222-2-222-2-2-2-2-2-222-2-2-2-22-22-2220000-2-2220000000022-2-2000000000000000000000000
χ252222222222-2-2-2-22222-2-2-2-22222-2-22-22-222-2-20000000022-2-20000000000000000000000000000
χ262222222222-2-2-2-22222-2-2-2-22222-2-22-22-2-2-22200000000-2-2220000000000000000000000000000
χ272222222222-2-2-2-222-2-2-2-2-2-222-2-222-22-2222-2-200000000-2-2220000000000000000000000000000
χ282222222222-2-2-2-222-2-2-2-2-2-222-2-222-22-22-2-2220000000022-2-20000000000000000000000000000
χ2922-2-2222-2-2-22222-2-222-2-2-2-222-2-222-2-22-20000000000000000000000000000000000002-22-20000
χ3022-2-2222-2-2-22222-2-222-2-2-2-222-2-222-2-22-2000000000000000000000000000000000000-22-220000
χ3122-2-2222-2-2-22222-2-2-2-2-2-2-2-22222-2-222-220000000000000000000000000000000000002i−2i−2i2i0000
χ3222-2-2222-2-2-22222-2-2-2-2-2-2-2-22222-2-222-22000000000000000000000000000000000000−2i2i2i−2i0000
χ3322-2-2222-2-2-222-2-22222-2-222-2-2-2-22-222-2-2000000000000000000000000000000002-22-200000000
χ3422-2-2222-2-2-222-2-22222-2-222-2-2-2-22-222-2-200000000000000000000000000000000-22-2200000000
χ3522-2-2222-2-2-222-2-222-2-2-2-222-2-222-22-2-222000000000000000000000000000000002i−2i−2i2i00000000
χ3622-2-2222-2-2-222-2-222-2-2-2-222-2-222-22-2-22200000000000000000000000000000000−2i2i2i−2i00000000
χ3722-2-2222-2-2-2-2-222222222-2-2-2-2-2-2-222-2-220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ3822-2-2222-2-2-2-2-222222222-2-2-2-2-2-2-222-2-22000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ3922-2-2222-2-2-2-2-22222-2-222-2-2-2-2222-2-222-200000000000000000000000022-2-2-2-222000000000000
χ4022-2-2222-2-2-2-2-22222-2-222-2-2-2-2222-2-222-2000000000000000000000000-2-22222-2-2000000000000
χ4122-2-2222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-222200000000000000000000000000000000000000002-22-2
χ4222-2-2222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-22220000000000000000000000000000000000000000-22-22
χ4322-2-2222-2-2-2-2-2-2-2-2-2-2-222222222222-2-2-200000000000000000000000000000000000000002i−2i−2i2i
χ4422-2-2222-2-2-2-2-2-2-2-2-2-2-222222222222-2-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ4544444-4-44-4-400004-40000004-400000000000000000000004-40000000000000000000000000000
χ4644444-4-44-4-400004-40000004-40000000000000000000000-440000000000000000000000000000
χ4744444-4-44-4-40000-44000000-44000000000000000000004-4000000000000000000000000000000
χ4844444-4-44-4-40000-44000000-4400000000000000000000-44000000000000000000000000000000
χ494444-44-4-44-4004-40000004-400000000000000000000000000004-4000000000000000000000000
χ504444-44-4-44-4004-40000004-40000000000000000000000000000-44000000000000000000000000
χ514444-44-4-44-400-44000000-44000000000000000000000000004-400000000000000000000000000
χ524444-44-4-44-400-44000000-4400000000000000000000000000-4400000000000000000000000000
χ534444-4-44-4-444-40000004-400000000000000000000000000000000004-400000000000000000000
χ544444-4-44-4-444-40000004-40000000000000000000000000000000000-4400000000000000000000
χ554444-4-44-4-44-44000000-44000000000000000000000000000000004-40000000000000000000000
χ564444-4-44-4-44-44000000-4400000000000000000000000000000000-440000000000000000000000
χ5744-4-44-4-4-44400004-4000000-4400000000004i−4i0000000000000000000000000000000000000000
χ5844-4-44-4-4-44400004-4000000-440000000000−4i4i0000000000000000000000000000000000000000
χ5944-4-44-4-4-4440000-440000004-4000000004i−4i000000000000000000000000000000000000000000
χ6044-4-44-4-4-4440000-440000004-400000000−4i4i000000000000000000000000000000000000000000
χ6144-4-4-44-44-44004-4000000-4400000000000000004i−4i000000000000000000000000000000000000
χ6244-4-4-44-44-44004-4000000-440000000000000000−4i4i000000000000000000000000000000000000
χ6344-4-4-44-44-4400-440000004-4000000000000004i−4i00000000000000000000000000000000000000
χ6444-4-4-44-44-4400-440000004-400000000000000−4i4i00000000000000000000000000000000000000
χ6544-4-4-4-4444-44-4000000-44000000000000000000004i−4i0000000000000000000000000000000000
χ6644-4-4-4-4444-44-4000000-4400000000000000000000−4i4i0000000000000000000000000000000000
χ6744-4-4-4-4444-4-440000004-400000000000000000000004i−4i00000000000000000000000000000000
χ6844-4-4-4-4444-4-440000004-40000000000000000000000−4i4i00000000000000000000000000000000
χ698-88i−8i0000000000004-40000004i−4i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000
χ708-88i−8i0000000000004-40000004i−4i000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000
χ718-88i−8i000000000000-44000000−4i4i0000000000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ000000000000
χ728-88i−8i000000000000-44000000−4i4i000000000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ000000000000
χ738-8−8i8i0000000000004-4000000−4i4i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000
χ748-8−8i8i0000000000004-4000000−4i4i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000
χ758-8−8i8i000000000000-440000004i−4i0000000000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3000000000000
χ768-8−8i8i000000000000-440000004i−4i000000000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3000000000000

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