Finite Group Databasebeta

← Group #101504

Character table — Group #101504

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888844444444448888888888884444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i1111-1-11-1-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i1111-1-11-1-1-1ii−i−iii−i−iii−i−i-1-111−i−iii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-1111-111−i−iiiii−i−i−i−iii11-1-1ii−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-1111-111−i−iiiii−i−i−i−iii-1-111−i−iii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii1111-1-11-1-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii1111-1-11-1-1-1−i−iii−i−iii−i−iii-1-111ii−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-1111-111ii−i−i−i−iiiii−i−i11-1-1−i−iii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-1111-111ii−i−i−i−iiiii−i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222-2-2-2-222222222000000-2-2000000-2-2-2-200000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000-2-2000000222200000000000000000000
χ192222222222-2-222-2-2-2-222220000000022-2-222-2-2-2-20000000000000000000000000000
χ202222222222-2-222-2-2-2-2222200000000-2-222-2-2-2-2220000000000000000000000000000
χ212222222222-2-222-2-2-2-2-2-2-2-20000000000000022002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ222222222222-2-222-2-2-2-2-2-2-2-2000000000000002200−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ2322222222-2-222-2-222-2-222-2-2000000000000002-20022220000-2-2-2-20000000000000000
χ2422222222-2-222-2-222-2-222-2-2000000000000002-200-2-2-2-2000022220000000000000000
χ2522222222-2-222-2-222-2-2-2-2220000000022-2-2-2-2-22220000000000000000000000000000
χ2622222222-2-222-2-222-2-2-2-22200000000-2-22222-22-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-22i2i2i2i−2i−2i−2i−2i000000-22000000−2i−2i2i2i00000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2−2i−2i−2i−2i2i2i2i2i000000-220000002i2i−2i−2i00000000000000000000
χ2922-22-2-2-222i−2i002i−2i00002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i002i−2i00002-21−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000000000
χ3022-22-2-2-222i−2i002i−2i00002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2i2i0000-22−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000000000000
χ3122-22-2-2-222i−2i002i−2i00002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i002i−2i00002-2−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000000000
χ3222-22-2-2-222i−2i002i−2i00002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2i2i0000-221−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000000000000
χ3322-22-2-2-222i−2i002i−2i0000−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i2-2002i−2i00001+i−1−i1−i−1+i−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000000000000
χ3422-22-2-2-222i−2i002i−2i0000−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i-2200−2i2i0000−1−i1+i−1+i1−i−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000000000000000
χ3522-22-2-2-222i−2i002i−2i0000−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-2002i−2i0000−1−i1+i−1+i1−i1+i−1−i1−i−1+i1+i−1−i1−i−1+i0000000000000000
χ3622-22-2-2-222i−2i002i−2i0000−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i-2200−2i2i00001+i−1−i1−i−1+i1+i−1−i1−i−1+i−1−i1+i−1+i1−i0000000000000000
χ3722-22-2-2-22−2i2i00−2i2i00002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i2-200−2i2i00001−i−1+i1+i−1−i−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000000000000000
χ3822-22-2-2-22−2i2i00−2i2i00002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i-22002i−2i0000−1+i1−i−1−i1+i−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000000000000000
χ3922-22-2-2-22−2i2i00−2i2i00002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-200−2i2i0000−1+i1−i−1−i1+i1−i−1+i1+i−1−i1−i−1+i1+i−1−i0000000000000000
χ4022-22-2-2-22−2i2i00−2i2i00002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i-22002i−2i00001−i−1+i1+i−1−i1−i−1+i1+i−1−i−1+i1−i−1−i1+i0000000000000000
χ4122-22-2-2-22−2i2i00−2i2i0000−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i002i−2i0000-22−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i0000000000000000
χ4222-22-2-2-22−2i2i00−2i2i0000−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2i2i00002-21+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000000000
χ4322-22-2-2-22−2i2i00−2i2i0000−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i002i−2i0000-221+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000000000000000
χ4422-22-2-2-22−2i2i00−2i2i0000−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2i2i00002-2−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000000000
χ452-22-22-2-222i−2i2i−2i−2i2i2i−2i2-200002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000002−2i2−i21−i−1+i1+i−1−i
χ462-22-22-2-222i−2i2i−2i−2i2i2i−2i2-200002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000000000−22−i2i2−1+i1−i−1−i1+i
χ472-22-22-2-222i−2i2i−2i−2i2i2i−2i2-20000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000002−2i2−i2−1+i1−i−1−i1+i
χ482-22-22-2-222i−2i2i−2i−2i2i2i−2i2-20000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000000000−22−i2i21−i−1+i1+i−1−i
χ492-22-22-2-22−2i2i−2i2i2i−2i−2i2i2-200002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000002−2−i2i2−1−i1+i−1+i1−i
χ502-22-22-2-22−2i2i−2i2i2i−2i−2i2i2-200002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000−22i2−i21+i−1−i1−i−1+i
χ512-22-22-2-22−2i2i−2i2i2i−2i−2i2i2-20000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000002−2−i2i21+i−1−i1−i−1+i
χ522-22-22-2-22−2i2i−2i2i2i−2i−2i2i2-20000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000−22i2−i2−1−i1+i−1+i1−i
χ5344-4-444-4-4004400-4-400000000000000000000000000000000000000002-22-200000000
χ5444-4-444-4-4004400-4-40000000000000000000000000000000000000000-22-2200000000
χ5544-4-444-4-400-4-4004400000000000000000000000000000000000000002i−2i−2i2i00000000
χ5644-4-444-4-400-4-400440000000000000000000000000000000000000000−2i2i2i−2i00000000
χ574-44-44-4-444i−4i−4i4i−4i4i−4i4i-4400000000000000000000000000000000000000000000000000
χ584-44-44-4-44−4i4i4i−4i4i−4i4i−4i-4400000000000000000000000000000000000000000000000000
χ594-4-444-44-4004i−4i00−4i4i0000000000000000000000000000000000002-22i−2i000000000000
χ604-4-444-44-4004i−4i00−4i4i000000000000000000000000000000000000-22−2i2i000000000000
χ614-4-444-44-400−4i4i004i−4i0000000000000000000000000000000000002-2−2i2i000000000000
χ624-4-444-44-400−4i4i004i−4i000000000000000000000000000000000000-222i−2i000000000000
χ634-4-4-4-44444400-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ644-4-4-4-44444400-4-400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ654-4-4-4-4444-4-400440000000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-4-4-4444-4-4004400000000−222222−2222−22−222200000000000000000000000000000000000000
χ67888-8-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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