Finite Group Databasebeta

← Group #97355

Character table — Group #97355

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222222244444444444444888888882244444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1111111111-111-1-1-1-11-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-11-1-111-1-1-11-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11-11111-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-1-1-1111111iiii−i−i−i−i1-11-11-1-1-1-11ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-1-1-1-1-1111111iiii−i−i−i−i-11-11-11-1-11-1ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-111-1-1-1-1-1-1111111−i−i−i−iiiii1-11-11-1-1-1-11−i−iii−i−iii−i−iii
χ1211111111-1-1-1-111-1-1-1-1-1-1111111−i−i−i−iiiii-11-11-11-1-11-1−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−i111-1-1111-1-1−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-1-1-111-11111−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiii111-1-1111-1-1ii−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-1-1-111-11111ii−i−iii−i−i−i−iii
χ17222222222222222-2-2-2-22-2-222-2-2000000000000002-200000000000000
χ18222222222222222-2-2-2-22-2-2-2-22200000000000000-2200000000000000
χ19222222222222-2-2-222-2-2-22-200000000000002002-2000-2000000000000
χ20222222222222-2-2-222-2-2-22-20000000000000-200-220002000000000000
χ21222222222222-2-2-2-2-222-2-2200000000000020-220000-20000000000000
χ22222222222222-2-2-2-2-222-2-22000000000000-202-2000020000000000000
χ2322222222-2-2-2-222-22222-2-2-222-2-200000000000000-2200000000000000
χ2422222222-2-2-2-222-22222-2-2-2-2-222000000000000002-200000000000000
χ2522222222-2-2-2-2-2-2222-2-22-2200000000000020-2-2000020000000000000
χ2622222222-2-2-2-2-2-2222-2-22-22000000000000-20220000-20000000000000
χ2722222222-2-2-2-2-2-22-2-22222-20000000000000200-2-20002000000000000
χ2822222222-2-2-2-2-2-22-2-22222-20000000000000-20022000-2000000000000
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
χ3344-4-44-44-40000000004i−4i00000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000
χ3444-4-44-44-40000000004i−4i0000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000
χ3544-4-44-44-4000000000−4i4i00000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000
χ3644-4-44-44-4000000000−4i4i0000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000
χ3744-4-4-44-4400000004i−4i0000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ3844-4-4-44-4400000004i−4i000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ3944-4-4-44-440000000−4i4i0000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ4044-4-4-44-440000000−4i4i000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ414-44-444-4-400004-400000000004i−4i000000000000000000000000000000
χ424-44-444-4-400004-40000000000−4i4i000000000000000000000000000000
χ434-44-444-4-40000-44000000004i−4i00000000000000000000000000000000
χ444-44-444-4-40000-4400000000−4i4i00000000000000000000000000000000
χ454-44-4-4-44400000040000-40000000000000000000000002i−2i2i−2i00000000
χ464-44-4-4-44400000040000-4000000000000000000000000−2i2i−2i2i00000000
χ474-44-4-4-444000000-4000040000000000000000000000002-2-2200000000
χ484-44-4-4-444000000-400004000000000000000000000000-222-200000000
χ494-4-444-4-444-44-40000000000000000000000000000000000002i−2i2i−2i0000
χ504-4-444-4-444-44-4000000000000000000000000000000000000−2i2i−2i2i0000
χ514-4-444-4-44-44-440000000000000000000000000000000000002-2-220000
χ524-4-444-4-44-44-44000000000000000000000000000000000000-222-20000
χ534-4-44-444-44-4-4400000000000000000000000000000000000000002-22-2
χ544-4-44-444-44-4-440000000000000000000000000000000000000000-22-22
χ554-4-44-444-4-444-400000000000000000000000000000000000000002i−2i−2i2i
χ564-4-44-444-4-444-40000000000000000000000000000000000000000−2i2i2i−2i

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