Finite Group Databasebeta

← Group #101643

Character table — Group #101643

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444422444444224444888888882244448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ711111111111111111111-1-111-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-1-1-1
χ811111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111
χ911111111-1-1-1-1111-1-1-11-1111-1-1-1ii−i−iii−i−i11-11-1-1i−ii−iii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1111-1-1-11-1111-1-1-1ii−i−iii−i−i-1-1-1111i−ii−i−i−iii-1-111−i−iii
χ1111111111-1-1-1-1111-1-1-11-1111-1-1-1−i−iii−i−iii11-11-1-1−ii−ii−i−iii11-1-1−i−iii
χ1211111111-1-1-1-1111-1-1-11-1111-1-1-1−i−iii−i−iii-1-1-1111−ii−iiii−i−i-1-111ii−i−i
χ1311111111-1-1-1-1111-1-1-11-1-1-11-111ii−i−i−i−iii111-1-1-1i−i−ii−i−iii-1-111ii−i−i
χ1411111111-1-1-1-1111-1-1-11-1-1-11-111ii−i−i−i−iii-1-11-111i−i−iiii−i−i11-1-1−i−iii
χ1511111111-1-1-1-1111-1-1-11-1-1-11-111−i−iiiii−i−i111-1-1-1−iii−iii−i−i-1-111−i−iii
χ1611111111-1-1-1-1111-1-1-11-1-1-11-111−i−iiiii−i−i-1-11-111−iii−i−i−iii11-1-1ii−i−i
χ1722222222222222-22-2-2-2200-2-20022220000000000-2-200000000000000
χ1822222222222222-22-2-2-2200-2-200-2-2-2-200000000002200000000000000
χ19222222222222-2-22-2-2-22-222-22220000000000-2-2000000000000000000
χ20222222222222-2-22-2-2-22-2-2-2-22-2-2000000000022000000000000000000
χ21222222222222-2-2-2-222-2-2002-2000000222200000000-2-2000000000000
χ22222222222222-2-2-2-222-2-2002-2000000-2-2-2-20000000022000000000000
χ2322222222-2-2-2-222-2-222-2-200-22002i2i−2i−2i0000000000−2i2i00000000000000
χ2422222222-2-2-2-222-2-222-2-200-2200−2i−2i2i2i00000000002i−2i00000000000000
χ2522222222-2-2-2-2-2-222222222-2-2-2-200000000002-2000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-2-2-2220000000000-22000000000000000000
χ2722222222-2-2-2-2-2-2-22-2-2-2200220000002i2i−2i−2i00000000−2i2i000000000000
χ2822222222-2-2-2-2-2-2-22-2-2-220022000000−2i−2i2i2i000000002i−2i000000000000
χ292-2-22-2-22222-2-22-202000-20000002i−2i2i−2i00000000000000i2−i2i2−i22−22−20000
χ302-2-22-2-22222-2-22-202000-20000002i−2i2i−2i00000000000000−i2i2−i2i2−22−220000
χ312-2-22-2-22222-2-22-202000-2000000−2i2i−2i2i00000000000000i2−i2i2−i2−22−220000
χ322-2-22-2-22222-2-22-202000-2000000−2i2i−2i2i00000000000000−i2i2−i2i22−22−20000
χ332-2-22-2-222-2-2222-20-200020000002-2-22000000000000002−2−222−2−220000
χ342-2-22-2-222-2-2222-20-200020000002-2-2200000000000000−222−2−222−20000
χ352-2-22-2-222-2-2222-20-20002000000-222-2000000000000002−2−22−222−20000
χ362-2-22-2-222-2-2222-20-20002000000-222-200000000000000−222−22−2−220000
χ37444-4-4-44-4000000004i−4i0000000000002+2i−2−2i2−2i−2+2i0000000000000000000000
χ38444-4-4-44-4000000004i−4i000000000000−2−2i2+2i−2+2i2−2i0000000000000000000000
χ39444-4-4-44-400000000−4i4i0000000000002−2i−2+2i2+2i−2−2i0000000000000000000000
χ40444-4-4-44-400000000−4i4i000000000000−2+2i2−2i−2−2i2+2i0000000000000000000000
χ4144-444-4-4-44i−4i4i−4i00000000000000000000002-2002i−2i0000000000000000
χ4244-444-4-4-44i−4i4i−4i0000000000000000000000-2200−2i2i0000000000000000
χ4344-444-4-4-4−4i4i−4i4i00000000000000000000002-200−2i2i0000000000000000
χ4444-444-4-4-4−4i4i−4i4i0000000000000000000000-22002i−2i0000000000000000
χ454-444-44-4-44i−4i−4i4i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ464-444-44-4-44i−4i−4i4i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ474-444-44-4-4−4i4i4i−4i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ484-444-44-4-4−4i4i4i−4i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ494-44-44-4-440000004000-4000004i−4i000000000000000000000000000000
χ504-44-44-4-440000004000-400000−4i4i000000000000000000000000000000
χ514-44-44-4-44000000-4000404-40000000000000000000000000000000000
χ524-44-44-4-44000000-400040-440000000000000000000000000000000000
χ534-4-44-4-44444-4-4-440-40004000000000000000000000000000000000000
χ544-4-44-4-444-4-444-4404000-4000000000000000000000000000000000000
χ5588-8-8-88-88000000000000000000000000000000000000000000000000
χ568-8-8-8888-8000000000000000000000000000000000000000000000000

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