Finite Group Databasebeta

← Group #100737

Character table — Group #100737

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444448888888888888888888888888881616161616161616161616163232
order12222222444444444422444444444888888888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-111-1-1-1-11-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111111-1-111-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-1-1-111111-111-1-11-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-1-1-1-1-111111-111-1-11-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-11
χ1111111111-1-1-1-1-1-1-1-111111-111-1-11-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−iii−i−i-1-111-11
χ1211111111-1-1-1-1-1-1-1-111111-111-1-11-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii−i−iii11-1-11-1
χ1311111111-1-1-1-1-1-1-1-111-1-11-1-1-111111ii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-11
χ1411111111-1-1-1-1-1-1-1-111-1-11-1-1-111111ii−i−iii−i−i−i−i−i−iiiii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1-1-1-1-1-1-111-1-11-1-1-111111−i−iii−i−iiiiiii−i−i−i−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-1-1-1-1-111-1-11-1-1-111111−i−iii−i−iiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-11
χ1722222222222222-2-2-2-2002-20000-2000000000022-2-222-2-200000000000000
χ1822222222222222-2-2-2-2002-20000-20000000000-2-222-2-22200000000000000
χ19222222222222-2-222-2-200-2-200002002222-2-2-2-20000000000000000000000
χ20222222222222-2-222-2-200-2-20000200-2-2-2-222220000000000000000000000
χ21222222222222-2-2-2-22222-22-2-222-2-2-2000000000000000000000000000000
χ22222222222222-2-2-2-222-2-2-2222-2-2-222000000000000000000000000000000
χ2322222222-2-2-2-222222222-2-2-2-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2-2222222-2-2-2-22222-2-2-2000000000000000000000000000000
χ2522222222-2-2-2-222-2-2-2-200-2200002002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2622222222-2-2-2-222-2-2-2-200-220000200−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ2722222222-2-2-2-2-2-222-2-200220000-200000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-222-2-200220000-20000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ2922-2-22-22-200002i−2i2i−2i2-200002i−2i2-20001+i−1−i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ3022-2-22-22-200002i−2i2i−2i2-200002i−2i2-2000−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ3122-2-22-22-200002i−2i2i−2i2-20000−2i2i-220001+i−1−i1−i−1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ3222-2-22-22-200002i−2i2i−2i2-20000−2i2i-22000−1−i1+i−1+i1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ3322-2-22-22-200002i−2i−2i2i-222-200000002i−2i1−i−1+i1+i−1−i−1+i1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ3422-2-22-22-200002i−2i−2i2i-222-200000002i−2i−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ3522-2-22-22-200002i−2i−2i2i-22-220000000−2i2i1−i−1+i1+i−1−i−1+i1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ3622-2-22-22-200002i−2i−2i2i-22-220000000−2i2i−1+i1−i−1−i1+i1−i−1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ3722-2-22-22-20000−2i2i2i−2i-222-20000000−2i2i1+i−1−i1−i−1+i−1−i1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ3822-2-22-22-20000−2i2i2i−2i-222-20000000−2i2i−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ3922-2-22-22-20000−2i2i2i−2i-22-2200000002i−2i1+i−1−i1−i−1+i−1−i1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ4022-2-22-22-20000−2i2i2i−2i-22-2200000002i−2i−1−i1+i−1+i1−i1+i−1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ4122-2-22-22-20000−2i2i−2i2i2-200002i−2i-220001−i−1+i1+i−1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ4222-2-22-22-20000−2i2i−2i2i2-200002i−2i-22000−1+i1−i−1−i1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ4322-2-22-22-20000−2i2i−2i2i2-20000−2i2i2-20001−i−1+i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ4422-2-22-22-20000−2i2i−2i2i2-20000−2i2i2-2000−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ45444-4-4-4-444i−4i4i−4i00000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ46444-4-4-4-444i−4i4i−4i0000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ47444-4-4-4-44−4i4i−4i4i00000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ48444-4-4-4-44−4i4i−4i4i0000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ494-4444-4-4-444-4-40000000000000000000000000000000002-22-20000000000
χ504-4444-4-4-444-4-4000000000000000000000000000000000-22-220000000000
χ514-4444-4-4-4-4-4440000000000000000000000000000000002i−2i−2i2i0000000000
χ524-4444-4-4-4-4-444000000000000000000000000000000000−2i2i2i−2i0000000000
χ534-44-4-444-44i−4i−4i4i000000000000000000000000000000000000000002-22i−2i00
χ544-44-4-444-44i−4i−4i4i00000000000000000000000000000000000000000-22−2i2i00
χ554-44-4-444-4−4i4i4i−4i000000000000000000000000000000000000000002-2−2i2i00
χ564-44-4-444-4−4i4i4i−4i00000000000000000000000000000000000000000-222i−2i00
χ5788-88-88-8-8000000000000000000000000000000000000000000000000000
χ588-8-88-8-888000000000000000000000000000000000000000000000000000
χ598-8-8-888-88000000000000000000000000000000000000000000000000000

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