Finite Group Databasebeta

← Group #97050

Character table — Group #97050

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888224444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-11-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i111-1-11-1-111-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1-1-111-1-111ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1111-1-1-1-111−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-111-11111-1-1−i−iii−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii111-1-11-1-111-1-1−i−iii−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1-111-1-111−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1111-1-1-1-111ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-111-11111-1-1ii−i−iii−i−i−i−iii
χ17222222222222-2-22222-2-2-2-222-2-2-2-2000000000000000002000-22-20000000000000000
χ18222222222222-2-22222-2-2-2-222-2-2-2-200000000000000000-20002-220000000000000000
χ192222222222-2-22222-2-222-2-2-2-222-2-2000000000000000020-22-20000000000000000000
χ202222222222-2-22222-2-222-2-2-2-222-2-20000000000000000-202-220000000000000000000
χ212222222222-2-2-2-222-2-2-2-222-2-2-2-2220000000000000000000000002-22-2000000000000
χ222222222222-2-2-2-222-2-2-2-222-2-2-2-222000000000000000000000000-22-22000000000000
χ2322222222-2-22222-2-2222222-2-2-2-2-2-20000000000000000000000002-2-22000000000000
χ2422222222-2-22222-2-2222222-2-2-2-2-2-2000000000000000000000000-222-2000000000000
χ2522222222-2-222-2-2-2-222-2-2-2-2-2-22222000000000000000020-2-220000000000000000000
χ2622222222-2-222-2-2-2-222-2-2-2-2-2-222220000000000000000-2022-20000000000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-222-2-222000000000000000002000-2-220000000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-222-2-22200000000000000000-200022-20000000000000000
χ2922-222-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-22-22i−2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3022-222-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-22-22i−2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3122-222-2-2-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i-222-2-22−2i2i00000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ3222-222-2-2-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i-222-2-22−2i2i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ3322-222-2-2-22i−2i−2i2i2i−2i2i−2i−2i2i2i−2i-22-222-2−2i2i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ3422-222-2-2-22i−2i−2i2i2i−2i2i−2i−2i2i2i−2i-22-222-2−2i2i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ3522-222-2-2-22i−2i−2i2i−2i2i2i−2i−2i2i−2i2i2-2-22-222i−2i2ζ2ζ2ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ32ζ32ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ3000000000000000000000000
χ3622-222-2-2-22i−2i−2i2i−2i2i2i−2i−2i2i−2i2i2-2-22-222i−2i−2ζ−2ζ−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ32ζ32ζ3000000000000000000000000
χ3722-222-2-2-2−2i2i2i−2i2i−2i−2i2i2i−2i2i−2i2-2-22-22−2i2i2ζ32ζ32ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ2ζ2ζ2ζ−2ζ−2ζ−2ζ−2ζ000000000000000000000000
χ3822-222-2-2-2−2i2i2i−2i2i−2i−2i2i2i−2i2i−2i2-2-22-22−2i2i−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ−2ζ−2ζ−2ζ2ζ2ζ2ζ2ζ000000000000000000000000
χ3922-222-2-2-2−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i-22-222-22i−2i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4022-222-2-2-2−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i-22-222-22i−2i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ4122-222-2-2-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i-222-2-222i−2i00000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ4222-222-2-2-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i-222-2-222i−2i0000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ4322-222-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-22-2−2i2i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ4422-222-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-22-2−2i2i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ45444-4-44-4-4440000-4-400000000000022-2-222-2-222-2-222-2-2000000000000000000000000
χ46444-4-44-4-4440000-4-4000000000000-2-222-2-222-2-222-2-222000000000000000000000000
χ47444-4-44-4-4-4-40000440000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ48444-4-44-4-4-4-4000044000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ4944-4-4-4-4444i−4i0000−4i4i0000000000002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3000000000000000000000000
χ5044-4-4-4-4444i−4i0000−4i4i000000000000−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3000000000000000000000000
χ5144-4-4-4-444−4i4i00004i−4i0000000000002ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ000000000000000000000000
χ5244-4-4-4-444−4i4i00004i−4i000000000000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ000000000000000000000000
χ534-444-4-44-400004i−4i0000−4i4i000000002ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ544-444-4-44-400004i−4i0000−4i4i00000000−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ554-444-4-44-40000−4i4i00004i−4i000000002ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ000000000000000000000000
χ564-444-4-44-40000−4i4i00004i−4i00000000−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ000000000000000000000000
χ574-44-44-4-44004i−4i0000−4i4i00000000002ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ584-44-44-4-44004i−4i0000−4i4i0000000000−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ594-44-44-4-4400−4i4i00004i−4i00000000002ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ000000000000000000000000
χ604-44-44-4-4400−4i4i00004i−4i0000000000−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ000000000000000000000000
χ614-4-44-44-440000440000-4-4000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ624-4-44-44-440000440000-4-400000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ634-4-44-44-440000-4-4000044000000002-22-2-22-222-22-2-22-22000000000000000000000000
χ644-4-44-44-440000-4-400004400000000-22-222-22-2-22-222-22-2000000000000000000000000
χ654-4-4-4444-400440000-4-400000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ664-4-4-4444-400440000-4-40000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ674-4-4-4444-400-4-400004400000000002-2-22-222-22-2-22-222-2000000000000000000000000
χ684-4-4-4444-400-4-40000440000000000-222-22-2-22-222-22-2-22000000000000000000000000

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