Finite Group Databasebeta

← Group #101494

Character table — Group #101494

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888844444444448888888888882244888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111-11-1iiii−i−i−i−i-111111-1-1-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-1111-11-1iiii−i−i−i−i-111111-1-1-1-1ii−i−iii−i−iii−i−i-1-111−i−iii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-1111-11-1iiii−i−i−i−i-11-1-1-1-11111−i−iiiii−i−i−i−iii11-1-1ii−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-1111-11-1iiii−i−i−i−i-11-1-1-1-11111−i−iiiii−i−i−i−iii-1-111−i−iii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-1111-11-1−i−i−i−iiiii-111111-1-1-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-1111-11-1−i−i−i−iiiii-111111-1-1-1-1−i−iii−i−iii−i−iii-1-111ii−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-1111-11-1−i−i−i−iiiii-11-1-1-1-11111ii−i−i−i−iiiii−i−i11-1-1−i−iii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-1111-11-1−i−i−i−iiiii-11-1-1-1-11111ii−i−i−i−iiiii−i−i-1-111ii−i−i11-1-1−i−iii
χ172222222222222222-222-2-2-222222222-2-2000000000000-2-2-2-200000000000000000000
χ182222222222222222-222-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000222200000000000000000000
χ192222222222-2-222-2-22-2-222200000000-2-222-2-222-2-20000000000000000000000000000
χ202222222222-2-222-2-22-2-222200000000-2-2-2-222-2-2220000000000000000000000000000
χ212222222222-2-222-2-2-2-2-2-2-2-20000000022000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ222222222222-2-222-2-2-2-2-2-2-2-2000000002200000000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ2322222222-2-222-2-2222-2-2-22-2000000002-222-2-2-2-2220000000000000000000000000000
χ2422222222-2-222-2-2222-2-2-22-2000000002-2-2-22222-2-20000000000000000000000000000
χ2522222222-2-222-2-222-2-2-22-2200000000-220000000022220000-2-2-2-20000000000000000
χ2622222222-2-222-2-222-2-2-22-2200000000-2200000000-2-2-2-2000022220000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2222-222i2i2i2i−2i−2i−2i−2i2-2000000000000−2i−2i2i2i00000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2222-22−2i−2i−2i−2i2i2i2i2i2-20000000000002i2i−2i−2i00000000000000000000
χ2922-2-222-2-22i−2i2i−2i2i−2i2i−2i02-20002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000000000000000002−2i2−i21+i−1−i1−i−1+i
χ3022-2-222-2-22i−2i2i−2i2i−2i2i−2i02-20002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000000000000000000−22−i2i2−1−i1+i−1+i1−i
χ3122-2-222-2-22i−2i2i−2i2i−2i2i−2i02-2000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000000000000000002−2i2−i2−1−i1+i−1+i1−i
χ3222-2-222-2-22i−2i2i−2i2i−2i2i−2i02-2000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000000000000000000−22−i2i21+i−1−i1−i−1+i
χ3322-2-222-2-2−2i2i−2i2i−2i2i−2i2i02-20002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000000000000000002−2−i2i2−1+i1−i−1−i1+i
χ3422-2-222-2-2−2i2i−2i2i−2i2i−2i2i02-20002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000000000000000000−22i2−i21−i−1+i1+i−1−i
χ3522-2-222-2-2−2i2i−2i2i−2i2i−2i2i02-2000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000000000000000002−2−i2i21−i−1+i1+i−1−i
χ3622-2-222-2-2−2i2i−2i2i−2i2i−2i2i02-2000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000000000000000000−22i2−i2−1+i1−i−1−i1+i
χ372-22-22-2-222200-2-200200-2-22i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i002−22−2i2−i2i2−i22−22−20000000000000000
χ382-22-22-2-222200-2-200200-2-22i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i00−22−22i2−i2i2−i2−22−220000000000000000
χ392-22-22-2-222200-2-200200-2-22−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i00−22−22−i2i2−i2i2−22−220000000000000000
χ402-22-22-2-222200-2-200200-2-22−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i002−22−2−i2i2−i2i22−22−20000000000000000
χ412-22-22-2-222200-2-200-20022-2i2−i2i2−i2i2−i2i2−i200002-2002-2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i20000000000000000
χ422-22-22-2-222200-2-200-20022-2i2−i2i2−i2i2−i2i2−i20000-2200-22−i2i2i2−i2−i2i2−i2i2i2−i2−i2i20000000000000000
χ432-22-22-2-222200-2-200-20022-2−i2i2−i2i2−i2i2−i2i200002-2002-2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i20000000000000000
χ442-22-22-2-222200-2-200-20022-2−i2i2−i2i2−i2i2−i2i20000-2200-22i2−i2−i2i2i2−i2i2−i2−i2i2i2−i20000000000000000
χ452-22-22-2-22-2-20022002002-2-22−22−2−22−22002i−2i00−2i2i00−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
χ462-22-22-2-22-2-20022002002-2-22−22−2−22−2200−2i2i002i−2i00i2−i2−i2i22−2−22i2−i2−i2i20000000000000000
χ472-22-22-2-22-2-20022002002-2-2−22−222−22−2002i−2i00−2i2i00i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
χ482-22-22-2-22-2-20022002002-2-2−22−222−22−200−2i2i002i−2i00−i2i2i2−i2−222−2−i2i2i2−i20000000000000000
χ492-22-22-2-22-2-2002200-200-2222−22−2−22−2200002-200-222−22−2−222−2−22−220000000000000000
χ502-22-22-2-22-2-2002200-200-2222−22−2−22−220000-22002-2−22−22−222−22−22−20000000000000000
χ512-22-22-2-22-2-2002200-200-222−22−222−22−200002-200-22−22−222−2−222−22−20000000000000000
χ522-22-22-2-22-2-2002200-200-222−22−222−22−20000-22002-22−22−22−2−22−22−220000000000000000
χ5344-4-444-4-44i−4i−4i4i4i−4i−4i4i0-440000000000000000000000000000000000000000000000000
χ5444-4-444-4-4−4i4i4i−4i−4i4i4i−4i0-440000000000000000000000000000000000000000000000000
χ554-44-4-444-4004i−4i00−4i4i0000000000000000000000000000000000002-22i−2i000000000000
χ564-44-4-444-4004i−4i00−4i4i000000000000000000000000000000000000-22−2i2i000000000000
χ574-44-4-444-400−4i4i004i−4i0000000000000000000000000000000000002-2−2i2i000000000000
χ584-44-4-444-400−4i4i004i−4i000000000000000000000000000000000000-222i−2i000000000000
χ594-4-444-44-44i−4i00−4i4i000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000
χ604-4-444-44-44i−4i00−4i4i00000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000
χ614-4-444-44-4−4i4i004i−4i000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000
χ624-4-444-44-4−4i4i004i−4i00000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000
χ634-4-44-44-44004400-4-400000000000000000000000000000000000000002i−2i2i−2i00000000
χ644-4-44-44-44004400-4-40000000000000000000000000000000000000000−2i2i−2i2i00000000
χ654-4-44-44-4400-4-4004400000000000000000000000000000000000000002-2-2200000000
χ664-4-44-44-4400-4-400440000000000000000000000000000000000000000-222-200000000
χ678888-8-8-8-8000000000000000000000000000000000000000000000000000000000000
χ6888-8-8-8-888000000000000000000000000000000000000000000000000000000000000

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