Finite Group Databasebeta

← Group #97368

Character table — Group #97368

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444444444888888882444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-1-1-1111111iiii−i−i−i−i1-11-1-1-11-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-1-1-1-1-1111111iiii−i−i−i−i-11-11-1-1-11-11ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-111-1-1-1-1-1-1111111−i−i−i−iiiii1-11-1-1-11-11-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-111-1-1-1-1-1-1111111−i−i−i−iiiii-11-11-1-1-11-11−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−i1-1-11111-1-11−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−i-111-111-111-1−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiii1-1-11111-1-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiii-111-111-111-1ii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-2-2-222-2-20000000000002-20000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222000000000000-220000000000000000
χ19222222222222-2-2-2-222-2-22-200000000000000220000-2-2000000000000
χ20222222222222-2-2-2-222-2-22-200000000000000-2-2000022000000000000
χ21222222222222-2-2-2-2-2-222-22000000000000220000-2-200000000000000
χ22222222222222-2-2-2-2-2-222-22000000000000-2-200002200000000000000
χ2322222222-2-2-2-222-2-22222-2-222-2-2000000000000-220000000000000000
χ2422222222-2-2-2-222-2-22222-2-2-2-2220000000000002-20000000000000000
χ2522222222-2-2-2-2-2-22222-2-2-220000000000002-20000-2200000000000000
χ2622222222-2-2-2-2-2-22222-2-2-22000000000000-2200002-200000000000000
χ2722222222-2-2-2-2-2-222-2-2222-2000000000000002-20000-22000000000000
χ2822222222-2-2-2-2-2-222-2-2222-200000000000000-2200002-2000000000000
χ294444-4-4-4-444-4-40000000000000022-2-222-2-20000000000000000000000
χ304444-4-4-4-444-4-400000000000000-2-222-2-2220000000000000000000000
χ314444-4-4-4-4-4-444000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ324444-4-4-4-4-4-44400000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ3344-4-444-4-400000000004i−4i0000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000
χ3444-4-444-4-400000000004i−4i000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000
χ3544-4-444-4-40000000000−4i4i0000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000
χ3644-4-444-4-40000000000−4i4i000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000
χ3744-4-4-4-444000000004i−4i000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ3844-4-4-4-444000000004i−4i00000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ3944-4-4-4-44400000000−4i4i000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ4044-4-4-4-44400000000−4i4i00000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ414-44-44-44-40000004i−4i00000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ424-44-44-44-40000004i−4i0000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ434-44-44-44-4000000−4i4i00000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ444-44-44-44-4000000−4i4i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ454-44-4-44-4400004-400000000004i−4i000000000000000000000000000000
χ464-44-4-44-4400004-40000000000−4i4i000000000000000000000000000000
χ474-44-4-44-440000-44000000004i−4i00000000000000000000000000000000
χ484-44-4-44-440000-4400000000−4i4i00000000000000000000000000000000
χ494-4-444-4-444i−4i4i−4i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ504-4-444-4-444i−4i4i−4i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ514-4-444-4-44−4i4i−4i4i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ524-4-444-4-44−4i4i−4i4i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ534-4-44-444-44i−4i−4i4i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ544-4-44-444-44i−4i−4i4i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ554-4-44-444-4−4i4i4i−4i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ564-4-44-444-4−4i4i4i−4i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000

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