Finite Group Databasebeta

← Group #101665

Character table — Group #101665

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444422444444444444888888884444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ7111111111111111111111-1-11-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-111-1111-1-1ii−i−iii−i−i1-111-1-1i−ii−i11-1-1ii−i−iii−i−i
χ1011111111-1-1-1-111-1-1-1-111-1111-1-1ii−i−iii−i−i1-1-1-111i−ii−i-1-111−i−iii−i−iii
χ1111111111-1-1-1-111-1-1-1-111-1111-1-1−i−iii−i−iii1-111-1-1−ii−ii11-1-1−i−iii−i−iii
χ1211111111-1-1-1-111-1-1-1-111-1111-1-1−i−iii−i−iii1-1-1-111−ii−ii-1-111ii−i−iii−i−i
χ1311111111-1-1-1-111-1-1-1-111-1-1-1111ii−i−i−i−iii-1111-1-1i−i−ii-1-111ii−i−i−i−iii
χ1411111111-1-1-1-111-1-1-1-111-1-1-1111ii−i−i−i−iii-11-1-111i−i−ii11-1-1−i−iiiii−i−i
χ1511111111-1-1-1-111-1-1-1-111-1-1-1111−i−iiiii−i−i-1111-1-1−iii−i-1-111−i−iiiii−i−i
χ1611111111-1-1-1-111-1-1-1-111-1-1-1111−i−iiiii−i−i-11-1-111−iii−i11-1-1ii−i−i−i−iii
χ172222222222222222-2-2-2-2-200-2000000222200000000-2-2000000000000
χ182222222222222222-2-2-2-2-200-2000000-2-2-2-20000000022000000000000
χ19222222222222-2-2-2-222-2-2-20020022220000000000-2-200000000000000
χ20222222222222-2-2-2-222-2-2-200200-2-2-2-200000000002200000000000000
χ21222222222222-2-2-2-2-2-222222-22200000000-2-200000000000000000000
χ22222222222222-2-2-2-2-2-2222-2-2-2-2-2000000002200000000000000000000
χ2322222222-2-2-2-222-2-222-2-2200-20000002i2i−2i−2i00000000−2i2i000000000000
χ2422222222-2-2-2-222-2-222-2-2200-2000000−2i−2i2i2i000000002i−2i000000000000
χ2522222222-2-2-2-2-2-2222222-222-2-2-200000000-2200000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-2-2-222000000002-200000000000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-22002002i2i−2i−2i0000000000−2i2i00000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-2200200−2i−2i2i2i00000000002i−2i00000000000000
χ29222-2-2-22-22i−2i2i−2i2-22i−2i000000000000002ζ3−2ζ32ζ−2ζ0000000000i2−i22−21+i−1−i1−i−1+i0000
χ30222-2-2-22-22i−2i2i−2i2-22i−2i000000000000002ζ3−2ζ32ζ−2ζ0000000000−i2i2−22−1−i1+i−1+i1−i0000
χ31222-2-2-22-22i−2i2i−2i2-22i−2i00000000000000−2ζ32ζ3−2ζ2ζ0000000000i2−i22−2−1−i1+i−1+i1−i0000
χ32222-2-2-22-22i−2i2i−2i2-22i−2i00000000000000−2ζ32ζ3−2ζ2ζ0000000000−i2i2−221+i−1−i1−i−1+i0000
χ33222-2-2-22-2−2i2i−2i2i2-2−2i2i000000000000002ζ−2ζ2ζ3−2ζ30000000000i2−i2−221−i−1+i1+i−1−i0000
χ34222-2-2-22-2−2i2i−2i2i2-2−2i2i000000000000002ζ−2ζ2ζ3−2ζ30000000000−i2i22−2−1+i1−i−1−i1+i0000
χ35222-2-2-22-2−2i2i−2i2i2-2−2i2i00000000000000−2ζ2ζ−2ζ32ζ30000000000i2−i2−22−1+i1−i−1−i1+i0000
χ36222-2-2-22-2−2i2i−2i2i2-2−2i2i00000000000000−2ζ2ζ−2ζ32ζ30000000000−i2i22−21−i−1+i1+i−1−i0000
χ37444-4-4-44-44i−4i4i−4i-44−4i4i0000000000000000000000000000000000000000
χ38444-4-4-44-4−4i4i−4i4i-444i−4i0000000000000000000000000000000000000000
χ3944-444-4-4-444-4-400000000000000000000000000000000000000002-22-2
χ4044-444-4-4-444-4-40000000000000000000000000000000000000000-22-22
χ4144-444-4-4-4-4-44400000000000000000000000000000000000000002i−2i−2i2i
χ4244-444-4-4-4-4-4440000000000000000000000000000000000000000−2i2i2i−2i
χ4344-4-4-44-444i−4i−4i4i0000000000000000000000002i−2i2-20000000000000000
χ4444-4-4-44-444i−4i−4i4i000000000000000000000000−2i2i-220000000000000000
χ4544-4-4-44-44−4i4i4i−4i0000000000000000000000002i−2i-220000000000000000
χ4644-4-4-44-44−4i4i4i−4i000000000000000000000000−2i2i2-20000000000000000
χ474-444-4-4-4400000000004-400004i−4i000000000000000000000000000000
χ484-444-4-4-4400000000004-40000−4i4i000000000000000000000000000000
χ494-444-4-4-440000000000-4404i−4i000000000000000000000000000000000
χ504-444-4-4-440000000000-440−4i4i000000000000000000000000000000000
χ514-4-44-444-4000000004i−4i000000002+2i−2−2i2−2i−2+2i00000000000000000000000000
χ524-4-44-444-4000000004i−4i00000000−2−2i2+2i−2+2i2−2i00000000000000000000000000
χ534-4-44-444-400000000−4i4i000000002−2i−2+2i2+2i−2−2i00000000000000000000000000
χ544-4-44-444-400000000−4i4i00000000−2+2i2−2i−2−2i2+2i00000000000000000000000000
χ558-88-888-8-8000000000000000000000000000000000000000000000000
χ568-8-8-88-888000000000000000000000000000000000000000000000000

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