Finite Group Databasebeta

← Group #97997

Character table — Group #97997

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111111111
χ51111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-11-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-111-1-11-11−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-111-1-11-11ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1111-1-11ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1-11−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11-111-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11-111-1ii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-2-20000222200000000000000000000-2-20000000000
χ18222222222222222222-2-2-2-2-2-2-20000-2-2-2-200000000000000000000220000000000
χ192222222222-2-222-2-2-2-222-2-222-22222000000000000000000000-20-2000000000000
χ202222222222-2-222-2-2-2-222-2-222-2-2-2-2-2000000000000000000000202000000000000
χ212222222222-2-222-2-2-2-2-2-222-2-2200000000000000000000000020-2000-2200000000
χ222222222222-2-222-2-2-2-2-2-222-2-22000000000000000000000000-2020002-200000000
χ2322222222-2-222-2-222-2-22222-2-2-222-2-2000000000000000000000-202000000000000
χ2422222222-2-222-2-222-2-22222-2-2-2-2-22200000000000000000000020-2000000000000
χ2522222222-2-222-2-222-2-2-2-2-2-2222000000000000000000000000202000-2-200000000
χ2622222222-2-222-2-222-2-2-2-2-2-2222000000000000000000000000-20-20002200000000
χ2722222222-2-2-2-2-2-2-2-222-2-22222-2000022-2-200000000000000000000-220000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22222-20000-2-222000000000000000000002-20000000000
χ2922-2-222-2-222-2-2-2-2222-2000000000002i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i20000000000002−22−2
χ3022-2-222-2-222-2-2-2-2222-2000000000002i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i2000000000000−22−22
χ3122-2-222-2-222-2-2-2-2222-200000000000−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i2000000000000−22−22
χ3222-2-222-2-222-2-2-2-2222-200000000000−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i20000000000002−22−2
χ3322-2-222-2-2-2-22222-2-22-2000000000002i−2i−2i2i0000000022−2−2−2−222000000000000−i2i2i2−i2
χ3422-2-222-2-2-2-22222-2-22-2000000000002i−2i−2i2i00000000−2−22222−2−2000000000000i2−i2−i2i2
χ3522-2-222-2-2-2-22222-2-22-200000000000−2i2i2i−2i0000000022−2−2−2−222000000000000i2−i2−i2i2
χ3622-2-222-2-2-2-22222-2-22-200000000000−2i2i2i−2i00000000−2−22222−2−2000000000000−i2i2i2−i2
χ372-22-22-22-22i−2i002i−2i00002-2002i−2i02-22i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ382-22-22-22-22i−2i002i−2i00002-2002i−2i02-22i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ392-22-22-22-22i−2i002i−2i00002-2002i−2i0-22−2i2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ402-22-22-22-22i−2i002i−2i00002-2002i−2i0-22−2i2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ412-22-22-22-2−2i2i00−2i2i00002-200−2i2i02-2−2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ422-22-22-22-2−2i2i00−2i2i00002-200−2i2i02-2−2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ432-22-22-22-2−2i2i00−2i2i00002-200−2i2i0-222i−2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ442-22-22-22-2−2i2i00−2i2i00002-200−2i2i0-222i−2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4544-4-444-4-44444-4-4-4-4-4400000000000000000000000000000000000000000000000
χ4644-4-444-4-4-4-4-4-44444-4400000000000000000000000000000000000000000000000
χ4744-4-4-4-4440000000000004i−4i000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ4844-4-4-4-4440000000000004i−4i00000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ4944-4-4-4-444000000000000−4i4i000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ5044-4-4-4-444000000000000−4i4i00000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ514-44-44-44-44i−4i004i−4i0000-4400−4i4i00000000000000000000000000000000000000000
χ524-44-44-44-4−4i4i00−4i4i0000-44004i−4i00000000000000000000000000000000000000000
χ534-44-4-44-44004i−4i004i−4i000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ544-44-4-44-44004i−4i004i−4i00000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ554-44-4-44-4400−4i4i00−4i4i000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ564-44-4-44-4400−4i4i00−4i4i00000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ574-4-444-4-444i−4i00−4i4i0000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ584-4-444-4-444i−4i00−4i4i000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ594-4-444-4-44−4i4i004i−4i0000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ604-4-444-4-44−4i4i004i−4i000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ614-4-44-444-4004i−4i00−4i4i000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ624-4-44-444-4004i−4i00−4i4i00000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ634-4-44-444-400−4i4i004i−4i000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ644-4-44-444-400−4i4i004i−4i00000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ658888-8-8-8-8000000000000000000000000000000000000000000000000000000000

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