Finite Group Databasebeta

← Group #100034

Character table — Group #100034

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222444444444444224444442244444488888888888888884444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ91111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i−i−i−i−iiiii-1-111−i−iii-1-111ii−i−i
χ111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iiiiiii−i−i−i−i-1-111ii−i−i-1-111−i−iii
χ121111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii
χ131111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−i-1-111−i−iii11-1-1−i−iii
χ141111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111−i−iii
χ151111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i11-1-1−i−iii-1-111ii−i−i
χ161111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−i−i−iiiii-1-111ii−i−i11-1-1ii−i−i
χ17222222222222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ192222222222-2-22222-2-222-2-2-2-222-2-222-2-222-2-200000000000000000000000000000000
χ202222222222-2-22222-2-222-2-2-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ2122222222-2-22222-2-22222-2-222-2-2-2-2000000002222-2-2-2-2000000000000000000000000
χ2222222222-2-22222-2-22222-2-222-2-2-2-200000000-2-2-2-22222000000000000000000000000
χ2322222222-2-222-2-2-2-222-2-222-2-222-2-20000000000000000000000000000000000002i−2i2i−2i
χ2422222222-2-222-2-2-2-222-2-222-2-222-2-2000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-2-2-222-2-2-2-22222-2-2-2-2220000000000000000000000000000000000002-2-22
χ2622222222-2-2-2-222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000-222-2
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2922-2-222-2-22-22i−2i2i−2i2-22i−2i2i−2i2-22-22i−2i2i−2i000000000000000000000000000000002-22i−2i0000
χ3022-2-222-2-22-22i−2i2i−2i2-22i−2i2i−2i2-22-22i−2i2i−2i00000000000000000000000000000000-22−2i2i0000
χ3122-2-222-2-22-22i−2i−2i2i2-22i−2i−2i2i-22-22−2i2i2i−2i0000000000000000000000002-22i−2i000000000000
χ3222-2-222-2-22-22i−2i−2i2i2-22i−2i−2i2i-22-22−2i2i2i−2i000000000000000000000000-22−2i2i000000000000
χ3322-2-222-2-22-2−2i2i2i−2i2-2−2i2i2i−2i-22-222i−2i−2i2i0000000000000000000000002-2−2i2i000000000000
χ3422-2-222-2-22-2−2i2i2i−2i2-2−2i2i2i−2i-22-222i−2i−2i2i000000000000000000000000-222i−2i000000000000
χ3522-2-222-2-22-2−2i2i−2i2i2-2−2i2i−2i2i2-22-2−2i2i−2i2i000000000000000000000000000000002-2−2i2i0000
χ3622-2-222-2-22-2−2i2i−2i2i2-2−2i2i−2i2i2-22-2−2i2i−2i2i00000000000000000000000000000000-222i−2i0000
χ3722-2-222-2-2-222i−2i2i−2i-222i−2i2i−2i-222-2−2i2i−2i2i00000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000
χ3822-2-222-2-2-222i−2i2i−2i-222i−2i2i−2i-222-2−2i2i−2i2i0000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000
χ3922-2-222-2-2-222i−2i−2i2i-222i−2i−2i2i2-2-222i−2i−2i2i00000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ4022-2-222-2-2-222i−2i−2i2i-222i−2i−2i2i2-2-222i−2i−2i2i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4122-2-222-2-2-22−2i2i2i−2i-22−2i2i2i−2i2-2-22−2i2i2i−2i00000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ4222-2-222-2-2-22−2i2i2i−2i-22−2i2i2i−2i2-2-22−2i2i2i−2i0000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ4322-2-222-2-2-22−2i2i−2i2i-22−2i2i−2i2i-222-22i−2i2i−2i00000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000
χ4422-2-222-2-2-22−2i2i−2i2i-22−2i2i−2i2i-222-22i−2i2i−2i0000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000
χ45444-4-4-44-40000440000-4-40000000000000000000000002-22-22-22-20000000000000000
χ46444-4-4-44-40000440000-4-4000000000000000000000000-22-22-22-220000000000000000
χ47444-4-4-44-40000-4-40000440000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ48444-4-4-44-40000-4-4000044000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ4944-44-4-4-4400004i−4i0000−4i4i0000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ5044-44-4-4-4400004i−4i0000−4i4i000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ5144-44-4-4-440000−4i4i00004i−4i0000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ5244-44-4-4-440000−4i4i00004i−4i000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ534-4444-4-4-4440000-4-40000000000004-400000000000000000000000000000000000000
χ544-4444-4-4-4440000-4-4000000000000-4400000000000000000000000000000000000000
χ554-4444-4-4-4-4-400004400000000000000004i−4i0000000000000000000000000000000000
χ564-4444-4-4-4-4-40000440000000000000000−4i4i0000000000000000000000000000000000
χ574-44-4-44-4400440000-4-400000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ584-44-4-44-4400440000-4-40000000000000000000000−2i22i2−2i22i2000000000000000000000000
χ594-44-4-44-4400-4-4000044000000000000000000000022−22−2222000000000000000000000000
χ604-44-4-44-4400-4-40000440000000000000000000000−222222−22000000000000000000000000
χ614-4-44-444-4004i−4i0000−4i4i0000000000000000002+2i−2−2i2−2i−2+2i0000000000000000000000000000
χ624-4-44-444-4004i−4i0000−4i4i000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000
χ634-4-44-444-400−4i4i00004i−4i0000000000000000002−2i−2+2i2+2i−2−2i0000000000000000000000000000
χ644-4-44-444-400−4i4i00004i−4i000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000
χ654-4-4-44-4444-40000-44000000000000004-4000000000000000000000000000000000000
χ664-4-4-44-4444-40000-4400000000000000-44000000000000000000000000000000000000
χ674-4-4-44-444-4400004-40000000000000000004-400000000000000000000000000000000
χ684-4-4-44-444-4400004-4000000000000000000-4400000000000000000000000000000000

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