Finite Group Databasebeta

← Group #125285

Character table — Group #125285

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ91111111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-222-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ192222222222-2-2-2-222-2-222-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2222222-2-222-2-222-2-200000000000000000000000000000000
χ2122-222-2-2-22-200002-200002i−2i22-2-2002i−2i002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ2222-222-2-2-22-200002-200002i−2i22-2-2002i−2i002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ2322-222-2-2-22-200002-200002i−2i-2-222002i−2i00−2i2i001+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i0000000000000000
χ2422-222-2-2-22-200002-200002i−2i-2-222002i−2i00−2i2i00−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i0000000000000000
χ2522-222-2-2-22-200002-20000−2i2i22-2-200−2i2i00−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ2622-222-2-2-22-200002-20000−2i2i22-2-200−2i2i00−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ2722-222-2-2-22-200002-20000−2i2i-2-22200−2i2i002i−2i001−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i0000000000000000
χ2822-222-2-2-22-200002-20000−2i2i-2-22200−2i2i002i−2i00−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i0000000000000000
χ292-222-22-2-2-2200002-2002i−2i2i−2i00002i−2i−2i2i2-2000000002ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ30000000000000000
χ302-222-22-2-2-2200002-2002i−2i2i−2i00002i−2i−2i2i2-200000000−2ζ2ζ−2ζ2ζ0000−2ζ32ζ3−2ζ32ζ30000000000000000
χ312-222-22-2-2-2200002-2002i−2i−2i2i00002i−2i2i−2i-2200002ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ300000000000000000000
χ322-222-22-2-2-2200002-2002i−2i−2i2i00002i−2i2i−2i-220000−2ζ2ζ−2ζ2ζ0000−2ζ32ζ3−2ζ32ζ300000000000000000000
χ332-222-22-2-2-2200002-200−2i2i2i−2i0000−2i2i−2i2i-2200002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ00000000000000000000
χ342-222-22-2-2-2200002-200−2i2i2i−2i0000−2i2i−2i2i-220000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ00000000000000000000
χ352-222-22-2-2-2200002-200−2i2i−2i2i0000−2i2i2i−2i2-2000000002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ0000000000000000
χ362-222-22-2-2-2200002-200−2i2i−2i2i0000−2i2i2i−2i2-200000000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ0000000000000000
χ372-2-22-2-2222222-2-2-2-22-22i−2i002i−2i2i−2i−2i2i000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ382-2-22-2-2222222-2-2-2-22-22i−2i002i−2i2i−2i−2i2i00000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ392-2-22-2-2222222-2-2-2-22-2−2i2i00−2i2i−2i2i2i−2i000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ402-2-22-2-2222222-2-2-2-22-2−2i2i00−2i2i−2i2i2i−2i00000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ412-2-22-2-22222-2-222-2-2-222i−2i00−2i2i−2i2i−2i2i000000000000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ422-2-22-2-22222-2-222-2-2-222i−2i00−2i2i−2i2i−2i2i00000000000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ432-2-22-2-22222-2-222-2-2-22−2i2i002i−2i2i−2i2i−2i000000000000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ442-2-22-2-22222-2-222-2-2-22−2i2i002i−2i2i−2i2i−2i00000000000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ452-2-22-2-222-2-222-2-222-220022000000-2-200002-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ462-2-22-2-222-2-222-2-222-220022000000-2-200002-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ472-2-22-2-222-2-222-2-222-2200-2-2000000220000-222−2−222−2−22−222−2−222−20000000000000000
χ482-2-22-2-222-2-222-2-222-2200-2-2000000220000-22−222−2−222−22−2−222−2−220000000000000000
χ492-2-22-2-222-2-2-2-222222-20022000000-2-20000-22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ502-2-22-2-222-2-2-2-222222-20022000000-2-20000-22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ512-2-22-2-222-2-2-2-222222-200-2-20000002200002-22−2−22−222−2−222−22−2−220000000000000000
χ522-2-22-2-222-2-2-2-222222-200-2-20000002200002-2−222−22−2−222−2−22−222−20000000000000000
χ5344444444-4-44444-4-4-4-400000000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ5544-444-4-4-4-440000-440044000000-4-40000000000000000000000000000000000000000
χ5644-444-4-4-4-440000-4400-4-4000000440000000000000000000000000000000000000000
χ5744-4-4-444-4004-44-4000000000000000000000000000000000000002i−2i2i−2i000000000000
χ5844-4-4-444-4004-44-400000000000000000000000000000000000000−2i2i−2i2i000000000000
χ5944-4-4-444-400-44-44000000000000000000000000000000000000002i−2i−2i2i000000000000
χ6044-4-4-444-400-44-4400000000000000000000000000000000000000−2i2i2i−2i000000000000
χ614-444-44-4-44-40000-440000004i−4i−4i4i000000000000000000000000000000000000000000
χ624-444-44-4-44-40000-44000000−4i4i4i−4i000000000000000000000000000000000000000000
χ634-44-44-44-4004-4-440000000000000000000000000000000000000000002i−2i2i−2i00000000
χ644-44-44-44-4004-4-44000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ654-44-44-44-400-444-40000000000000000000000000000000000000000002i−2i−2i2i00000000
χ664-44-44-44-400-444-4000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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