Finite Group Databasebeta

← Group #97691

Character table — Group #97691

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222444444444444224444444444444488888888888888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ911111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111ii−i−i−i−iii
χ1111111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111−i−iiiii−i−i
χ1211111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1311111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111−i−iii−i−iii
χ1411111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1611111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111ii−i−iii−i−i
χ1722222222222222-2-222-2-2-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000
χ192222222222-2-2-2-2222222-2-222-2-2-2-20000000000000000000000002-22-2000000000000
χ202222222222-2-2-2-2222222-2-222-2-2-2-2000000000000000000000000-22-22000000000000
χ212222222222-2-2-2-2-2-222-2-222-2-222-2-200000000000000000000000000002-22-200000000
χ222222222222-2-2-2-2-2-222-2-222-2-222-2-20000000000000000000000000000-22-2200000000
χ2322222222-2-2222222-2-222-2-2-2-222-2-222-2-222-2-200000000000000000000000000000000
χ2422222222-2-2222222-2-222-2-2-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-22222-2-2-2-22200000000000000000000000000002-2-2200000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2220000000000000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000002-2-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000-222-2000000000000
χ2922-22-2-22-22i−2i22-2-22i−2i2i−2i2i−2i2-22-22i−2i2i−2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3022-22-2-22-22i−2i22-2-22i−2i2i−2i2i−2i2-22-22i−2i2i−2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3122-22-2-22-22i−2i22-2-2−2i2i2i−2i−2i2i-22-22−2i2i2i−2i00000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000
χ3222-22-2-22-22i−2i22-2-2−2i2i2i−2i−2i2i-22-22−2i2i2i−2i0000000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000
χ3322-22-2-22-22i−2i-2-2222i−2i2i−2i2i−2i-222-2−2i2i−2i2i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ3422-22-2-22-22i−2i-2-2222i−2i2i−2i2i−2i-222-2−2i2i−2i2i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ3522-22-2-22-22i−2i-2-222−2i2i2i−2i−2i2i2-2-222i−2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000000000000
χ3622-22-2-22-22i−2i-2-222−2i2i2i−2i−2i2i2-2-222i−2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000000000000
χ3722-22-2-22-2−2i2i22-2-22i−2i−2i2i2i−2i-22-222i−2i−2i2i00000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000
χ3822-22-2-22-2−2i2i22-2-22i−2i−2i2i2i−2i-22-222i−2i−2i2i0000000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000
χ3922-22-2-22-2−2i2i22-2-2−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ4022-22-2-22-2−2i2i22-2-2−2i2i−2i2i−2i2i2-22-2−2i2i−2i2i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ4122-22-2-22-2−2i2i-2-2222i−2i−2i2i2i−2i2-2-22−2i2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000000000000
χ4222-22-2-22-2−2i2i-2-2222i−2i−2i2i2i−2i2-2-22−2i2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000000000000
χ4322-22-2-22-2−2i2i-2-222−2i2i−2i2i−2i2i-222-22i−2i2i−2i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4422-22-2-22-2−2i2i-2-222−2i2i−2i2i−2i2i-222-22i−2i2i−2i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ45444-44-4-4-444000000-4-4000000000000000000000000002-22-22-22-20000000000000000
χ46444-44-4-4-444000000-4-400000000000000000000000000-22-22-22-220000000000000000
χ47444-44-4-4-4-4-400000044000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ48444-44-4-4-4-4-40000004400000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ4944-4-4-44-444i−4i000000−4i4i000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ5044-4-4-44-444i−4i000000−4i4i00000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ5144-4-4-44-44−4i4i0000004i−4i000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ5244-4-4-44-44−4i4i0000004i−4i00000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ534-444-4-4-44004-44-40000000000000000004i−4i0000000000000000000000000000000000
χ544-444-4-4-44004-44-4000000000000000000−4i4i0000000000000000000000000000000000
χ554-444-4-4-4400-44-4400000000000000004i−4i000000000000000000000000000000000000
χ564-444-4-4-4400-44-440000000000000000−4i4i000000000000000000000000000000000000
χ574-44-4-444-40000004i−4i00−4i4i00000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ584-44-4-444-40000004i−4i00−4i4i0000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ594-44-4-444-4000000−4i4i004i−4i00000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ604-44-4-444-4000000−4i4i004i−4i0000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ614-4-4444-4-4004-4-44000000000000004i−4i00000000000000000000000000000000000000
χ624-4-4444-4-4004-4-4400000000000000−4i4i00000000000000000000000000000000000000
χ634-4-4444-4-400-444-4000000000000000000004i−4i00000000000000000000000000000000
χ644-4-4444-4-400-444-400000000000000000000−4i4i00000000000000000000000000000000
χ654-4-4-44-4440000004400-4-400000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ664-4-4-44-4440000004400-4-40000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ674-4-4-44-444000000-4-4004400000000000000002-2-222-2-22000000000000000000000000
χ684-4-4-44-444000000-4-400440000000000000000-222-2-222-2000000000000000000000000

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