Finite Group Databasebeta

← Group #125259

Character table — Group #125259

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444422444488888888888888884444444488888888
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
χ51111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ61111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222222222222222-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2222222-2-2-2-2-2-222-2-200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-22222-2-2-2-222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-200000000000000000000000000000000
χ2122-2-2-222-22-22-200000000002i2i−2i−2i2i2i−2i−2i00002-200002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000000
χ2222-2-2-222-22-22-200000000002i2i−2i−2i2i2i−2i−2i00002-20000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000000
χ2322-2-2-222-22-22-200000000002i2i−2i−2i−2i−2i2i2i0000-222ζ32ζ3−2ζ3−2ζ3000000002ζ2ζ−2ζ−2ζ0000000000000000
χ2422-2-2-222-22-22-200000000002i2i−2i−2i−2i−2i2i2i0000-22−2ζ3−2ζ32ζ32ζ300000000−2ζ−2ζ2ζ2ζ0000000000000000
χ2522-2-2-222-22-22-20000000000−2i−2i2i2i2i2i−2i−2i0000-222ζ2ζ−2ζ−2ζ000000002ζ32ζ3−2ζ3−2ζ30000000000000000
χ2622-2-2-222-22-22-20000000000−2i−2i2i2i2i2i−2i−2i0000-22−2ζ−2ζ2ζ2ζ00000000−2ζ3−2ζ32ζ32ζ30000000000000000
χ2722-2-2-222-22-22-20000000000−2i−2i2i2i−2i−2i2i2i00002-200002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000000
χ2822-2-2-222-22-22-20000000000−2i−2i2i2i−2i−2i2i2i00002-20000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000000
χ292-222-22-2-22-2-222i2i−2i−2i00002i−2i2-22-20000002i−2i00i2−i2i2−i22−22−22−22−2i2−i2i2−i20000000000000000
χ302-222-22-2-22-2-222i2i−2i−2i00002i−2i2-22-20000002i−2i00−i2i2−i2i2−22−22−22−22−i2i2−i2i20000000000000000
χ312-222-22-2-22-2-222i2i−2i−2i00002i−2i-22-22000000−2i2i002−22−2−i2i2−i2i2i2−i2i2−i2−22−220000000000000000
χ322-222-22-2-22-2-222i2i−2i−2i00002i−2i-22-22000000−2i2i00−22−22i2−i2i2−i2−i2i2−i2i22−22−20000000000000000
χ332-222-22-2-22-2-22−2i−2i2i2i0000−2i2i2-22-2000000−2i2i00i2−i2i2−i2−22−22−22−22i2−i2i2−i20000000000000000
χ342-222-22-2-22-2-22−2i−2i2i2i0000−2i2i2-22-2000000−2i2i00−i2i2−i2i22−22−22−22−2−i2i2−i2i20000000000000000
χ352-222-22-2-22-2-22−2i−2i2i2i0000−2i2i-22-220000002i−2i002−22−2i2−i2i2−i2−i2i2−i2i2−22−220000000000000000
χ362-222-22-2-22-2-22−2i−2i2i2i0000−2i2i-22-220000002i−2i00−22−22−i2i2−i2i2i2−i2i2−i22−22−20000000000000000
χ372-222-22-2-2-222-22i2i−2i−2i22-2-2−2i2i00002i−2i2i−2i0000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ382-222-22-2-2-222-22i2i−2i−2i22-2-2−2i2i00002i−2i2i−2i000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ392-222-22-2-2-222-22i2i−2i−2i-2-222−2i2i0000−2i2i−2i2i0000000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i
χ402-222-22-2-2-222-22i2i−2i−2i-2-222−2i2i0000−2i2i−2i2i000000000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i
χ412-222-22-2-2-222-2−2i−2i2i2i22-2-22i−2i0000−2i2i−2i2i0000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ422-222-22-2-2-222-2−2i−2i2i2i22-2-22i−2i0000−2i2i−2i2i000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ432-222-22-2-2-222-2−2i−2i2i2i-2-2222i−2i00002i−2i2i−2i0000000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ442-222-22-2-2-222-2−2i−2i2i2i-2-2222i−2i00002i−2i2i−2i000000000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ452-2-2-222-2222-2-200002i−2i2i−2i002i−2i−2i2i00002-200001+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i0000000000000000
χ462-2-2-222-2222-2-200002i−2i2i−2i002i−2i−2i2i00002-20000−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i0000000000000000
χ472-2-2-222-2222-2-200002i−2i2i−2i00−2i2i2i−2i0000-2200001−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i0000000000000000
χ482-2-2-222-2222-2-200002i−2i2i−2i00−2i2i2i−2i0000-220000−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i0000000000000000
χ492-2-2-222-2222-2-20000−2i2i−2i2i002i−2i−2i2i0000-2200001+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i0000000000000000
χ502-2-2-222-2222-2-20000−2i2i−2i2i002i−2i−2i2i0000-220000−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i0000000000000000
χ512-2-2-222-2222-2-20000−2i2i−2i2i00−2i2i2i−2i00002-200001−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i0000000000000000
χ522-2-2-222-2222-2-20000−2i2i−2i2i00−2i2i2i−2i00002-20000−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i0000000000000000
χ5344444444-4-4-4-444440000-4-40000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ55444-4-4-4-4400004i−4i4i−4i00000000000000000000000000000000000000002-22i−2i00000000
χ56444-4-4-4-4400004i−4i4i−4i0000000000000000000000000000000000000000-22−2i2i00000000
χ57444-4-4-4-440000−4i4i−4i4i00000000000000000000000000000000000000002-2−2i2i00000000
χ58444-4-4-4-440000−4i4i−4i4i0000000000000000000000000000000000000000-222i−2i00000000
χ5944-4-4-444-4-44-4400004i−4i−4i4i000000000000000000000000000000000000000000000000
χ6044-4-4-444-4-44-440000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ614-44-44-44-400004-4-440000000000000000000000000000000000002i−2i2i−2i000000000000
χ624-44-44-44-400004-4-44000000000000000000000000000000000000−2i2i−2i2i000000000000
χ634-44-44-44-40000-444-40000000000000000000000000000000000002i−2i−2i2i000000000000
χ644-44-44-44-40000-444-4000000000000000000000000000000000000−2i2i2i−2i000000000000
χ654-4-4-444-44-4-444000000000000004-4-4400000000000000000000000000000000000000
χ664-4-4-444-44-4-44400000000000000-444-400000000000000000000000000000000000000
χ6788-888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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