Finite Group Databasebeta

← Group #101359

Character table — Group #101359

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888822244444448888888888882244888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i-11111-1-1-1-11ii−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i-11111-1-1-1-11ii−i−iiiii−i−i−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-1-1-1-1-111111ii−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-1-111111ii−i−i−i−i−i−iiiii-1-111−i−iii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii-11111-1-1-1-11−i−iii−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii-11111-1-1-1-11−i−iii−i−i−i−iiiii-1-111ii−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-1-111111−i−iiiiiii−i−i−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-1-1-1-1-111111−i−iiiiiii−i−i−i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222-2-2-2-222222222-200000000-2-2-2-2-2000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-200000000-22222000000000000000000000000
χ192222222222-2-2-2-222-2-2222200000000-222-2-222-2-2-20000000000000000000000000000
χ202222222222-2-2-2-222-2-2222200000000-2-2-222-2-222-20000000000000000000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-200000000200000000200002i2i−2i−2i2i2i−2i−2i0000000000000000
χ222222222222-2-2-2-222-2-2-2-2-2-20000000020000000020000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-22222-2-2-2-222-2-200000000-2000000002000022-2-2-2-2220000000000000000
χ2422222222-2-22222-2-2-2-222-2-200000000-20000000020000-2-22222-2-20000000000000000
χ2522222222-2-22222-2-2-2-2-2-22200000000222-2-2-2-222-20000000000000000000000000000
χ2622222222-2-22222-2-2-2-2-2-222000000002-2-22222-2-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-22i2i2i2i−2i−2i−2i−2i200000000-2−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2−2i−2i−2i−2i2i2i2i2i200000000-22i2i−2i−2i000000000000000000000000
χ29222-2-2-22-22i−2i00002i−2i002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i0002i−2i002-201+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ30222-2-2-22-22i−2i00002i−2i002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i000−2i2i00-2201+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ31222-2-2-22-22i−2i00002i−2i002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i0002i−2i002-20−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ32222-2-2-22-22i−2i00002i−2i002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i000−2i2i00-220−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ33222-2-2-22-22i−2i00002i−2i00−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i02-2002i−2i000−1−i1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ34222-2-2-22-22i−2i00002i−2i00−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i0-2200−2i2i000−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ35222-2-2-22-22i−2i00002i−2i00−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i02-2002i−2i0001+i−1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ36222-2-2-22-22i−2i00002i−2i00−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i0-2200−2i2i0001+i−1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ37222-2-2-22-2−2i2i0000−2i2i002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i02-200−2i2i000−1+i1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ38222-2-2-22-2−2i2i0000−2i2i002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i0-22002i−2i000−1+i1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ39222-2-2-22-2−2i2i0000−2i2i002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i02-200−2i2i0001−i−1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ40222-2-2-22-2−2i2i0000−2i2i002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i0-22002i−2i0001−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ41222-2-2-22-2−2i2i0000−2i2i00−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i0002i−2i00-2201−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ42222-2-2-22-2−2i2i0000−2i2i00−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i000−2i2i002-201−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ43222-2-2-22-2−2i2i0000−2i2i00−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i0002i−2i00-220−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ44222-2-2-22-2−2i2i0000−2i2i00−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i000−2i2i002-20−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4522-222-2-2-22i−2i2i2i−2i−2i−2i2i2-200002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000002−2i2−i21−i−1+i1+i−1−i
χ4622-222-2-2-22i−2i2i2i−2i−2i−2i2i2-200002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000000000−22−i2i2−1+i1−i−1−i1+i
χ4722-222-2-2-22i−2i2i2i−2i−2i−2i2i2-20000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000002−2i2−i2−1+i1−i−1−i1+i
χ4822-222-2-2-22i−2i2i2i−2i−2i−2i2i2-20000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000000000−22−i2i21−i−1+i1+i−1−i
χ4922-222-2-2-2−2i2i−2i−2i2i2i2i−2i2-200002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000002−2−i2i2−1−i1+i−1+i1−i
χ5022-222-2-2-2−2i2i−2i−2i2i2i2i−2i2-200002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000−22i2−i21+i−1−i1−i−1+i
χ5122-222-2-2-2−2i2i−2i−2i2i2i2i−2i2-20000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000002−2−i2i21+i−1−i1−i−1+i
χ5222-222-2-2-2−2i2i−2i−2i2i2i2i−2i2-20000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000−22i2−i2−1−i1+i−1+i1−i
χ5344-444-4-4-44i−4i−4i−4i4i4i−4i4i-4400000000000000000000000000000000000000000000000000
χ5444-444-4-4-4−4i4i4i4i−4i−4i4i−4i-4400000000000000000000000000000000000000000000000000
χ5544-4-4-44-44440000-4-40000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5644-4-4-44-44440000-4-4000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5744-4-4-44-44-4-400004400000022−22−2222−222222−2200000000000000000000000000000000000000
χ5844-4-4-44-44-4-4000044000000−222222−2222−22−222200000000000000000000000000000000000000
χ594-444-44-4-4004i−4i4i−4i0000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ604-444-44-4-4004i−4i4i−4i000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ614-444-44-4-400−4i4i−4i4i0000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ624-444-44-4-400−4i4i−4i4i000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ634-4-44-4-444004-4-44000000000000000000000000000000000000002-22-2000000000000
χ644-4-44-4-444004-4-4400000000000000000000000000000000000000-22-22000000000000
χ654-4-44-4-44400-444-4000000000000000000000000000000000000002-2-22000000000000
χ664-4-44-4-44400-444-400000000000000000000000000000000000000-222-2000000000000
χ678-88-88-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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