Finite Group Databasebeta

← Group #96993

Character table — Group #96993

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222444444444444444488888888222444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-111-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-111-1-11-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111111-1-1-1-1
χ911111111-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−i111-1-11-11-1-1-11ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−i11-111-11-11-1-1-1ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−i-1-11-111-1-1111-1−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−i-1-1-11-1-111-1111−i−iii−i−iiiii−i−i
χ1311111111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii111-1-11-11-1-1-11−i−iii−i−iii−i−iii
χ1411111111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii11-111-11-11-1-1-1−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii-1-11-111-1-1111-1ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii-1-1-11-1-111-1111ii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-2-2-2-2-2220000000000220-2-200000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2220000000000-2-202200000000000000000
χ19222222222222-2-222-2-2-2-222-2-2000000002-200000002-20000000000000
χ20222222222222-2-222-2-2-2-222-2-200000000-220000000-220000000000000
χ21222222222222-2-2-2-22222-2-2-2-2000000000000200-2-2002000000000000
χ22222222222222-2-2-2-22222-2-2-2-2000000000000-2002200-2000000000000
χ2322222222-2-2-2-222-2-2-2-22222-2-200000000002-20-2200000000000000000
χ2422222222-2-2-2-222-2-2-2-22222-2-20000000000-2202-200000000000000000
χ2522222222-2-2-2-2-2-222-2-222-2-222000000002-20000000-220000000000000
χ2622222222-2-2-2-2-2-222-2-222-2-22200000000-2200000002-20000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-222220000000000002002-200-2000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22222000000000000-200-22002000000000000
χ2922-22-22-2-22i−2i2i−2i2-22-22-22i−2i2i−2i2i−2i00000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3022-22-22-2-22i−2i2i−2i2-22-22-22i−2i2i−2i2i−2i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3122-22-22-2-22i−2i2i−2i2-2-22-22−2i2i−2i2i2i−2i000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ3222-22-22-2-22i−2i2i−2i2-2-22-22−2i2i−2i2i2i−2i00000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ3322-22-22-2-22i−2i2i−2i-222-2-22−2i2i2i−2i−2i2i0000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ3422-22-22-2-22i−2i2i−2i-222-2-22−2i2i2i−2i−2i2i000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ3522-22-22-2-22i−2i2i−2i-22-222-22i−2i−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000000000000
χ3622-22-22-2-22i−2i2i−2i-22-222-22i−2i−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000000000000
χ3722-22-22-2-2−2i2i−2i2i2-22-22-2−2i2i−2i2i−2i2i00000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ3822-22-22-2-2−2i2i−2i2i2-22-22-2−2i2i−2i2i−2i2i0000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ3922-22-22-2-2−2i2i−2i2i2-2-22-222i−2i2i−2i−2i2i000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ4022-22-22-2-2−2i2i−2i2i2-2-22-222i−2i2i−2i−2i2i00000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ4122-22-22-2-2−2i2i−2i2i-222-2-222i−2i−2i2i2i−2i0000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ4222-22-22-2-2−2i2i−2i2i-222-2-222i−2i−2i2i2i−2i000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ4322-22-22-2-2−2i2i−2i2i-22-222-2−2i2i2i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000000000000
χ4422-22-22-2-2−2i2i−2i2i-22-222-2−2i2i2i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000000000000
χ454-444-4-44-44i−4i−4i4i0000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ464-444-4-44-44i−4i−4i4i000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ474-444-4-44-4−4i4i4i−4i0000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ484-444-4-44-4−4i4i4i−4i000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ494-4-444-4-4444-4-40000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ504-4-444-4-4444-4-4000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ514-4-444-4-44-4-4440000000000002-2-222-2-22000000000000000000000000
χ524-4-444-4-44-4-444000000000000-222-2-222-2000000000000000000000000
χ53888-88-8-8-8000000000000000000000000000000000000000000000000
χ5488-8-8-8-888000000000000000000000000000000000000000000000000
χ558-88-8-88-88000000000000000000000000000000000000000000000000
χ568-8-8-8888-8000000000000000000000000000000000000000000000000

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