Finite Group Databasebeta

← Group #112372

Character table — Group #112372

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222444422444444444488888888444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ911111111-1-1-1-1-1-11111-111-1-1-1iiii−i−i−i−i11-1-1111-1-1-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-11111-111-1-1-1iiii−i−i−i−i11-1-1-1-1-1111-11ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-1-1-11111-111-1-1-1iiii−i−i−i−i-1-11111-11-1-1-11−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1-1-11111-111-1-1-1iiii−i−i−i−i-1-111-1-11-1111-1−i−iii−i−iiiii−i−i
χ1311111111-1-1-1-1-1-11111-111-1-1-1−i−i−i−iiiii11-1-1111-1-1-11-1−i−iii−i−iii−i−iii
χ1411111111-1-1-1-1-1-11111-111-1-1-1−i−i−i−iiiii11-1-1-1-1-1111-11−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-1-1-11111-111-1-1-1−i−i−i−iiiii-1-11111-11-1-1-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-1-1-11111-111-1-1-1−i−i−i−iiiii-1-111-1-11-1111-1ii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-2-2-2-2-2000000000000002-200-22000000000000
χ182222222222222222-2-2-2-2-2-2-2-200000000000000-22002-2000000000000
χ19222222222222-2-2-2-222-2-2-22-22000000002-22-200000000000000000000
χ20222222222222-2-2-2-222-2-2-22-2200000000-22-2200000000000000000000
χ21222222222222-2-2-2-2-2-2222-22-20000000000002-2002-200000000000000
χ22222222222222-2-2-2-2-2-2222-22-2000000000000-2200-2200000000000000
χ2322222222-2-2-2-222-2-2222-2-2-22-2000000002-2-2200000000000000000000
χ2422222222-2-2-2-222-2-2222-2-2-22-200000000-222-200000000000000000000
χ2522222222-2-2-2-222-2-2-2-2-2222-220000000000002-200-2200000000000000
χ2622222222-2-2-2-222-2-2-2-2-2222-22000000000000-22002-200000000000000
χ2722222222-2-2-2-2-2-222-2-22-2-2222000000000000002200-2-2000000000000
χ2822222222-2-2-2-2-2-222-2-22-2-222200000000000000-2-20022000000000000
χ292-2-2-2-222222-2-22-22-22-222-2-2-220000000000000000000000002i−2i2i−2i0000
χ302-2-2-2-222222-2-22-22-22-222-2-2-22000000000000000000000000−2i2i−2i2i0000
χ312-2-2-2-222222-2-22-22-2-22-2-2222-2000000000000000000002i−2i2i−2i00000000
χ322-2-2-2-222222-2-22-22-2-22-2-2222-200000000000000000000−2i2i−2i2i00000000
χ332-2-2-2-222222-2-2-22-222-2-2-22-22200000000000000000000000000002-22-2
χ342-2-2-2-222222-2-2-22-222-2-2-22-2220000000000000000000000000000-22-22
χ352-2-2-2-222222-2-2-22-22-2222-22-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ362-2-2-2-222222-2-2-22-22-2222-22-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ372-2-2-2-2222-2-2222-2-222-22-222-2-200000000000000000000000000002i−2i−2i2i
χ382-2-2-2-2222-2-2222-2-222-22-222-2-20000000000000000000000000000−2i2i2i−2i
χ392-2-2-2-2222-2-2222-2-22-22-22-2-22222-2-2-2-222000000000000000000000000
χ402-2-2-2-2222-2-2222-2-22-22-22-2-222-2-22222-2-2000000000000000000000000
χ412-2-2-2-2222-2-222-222-22-2-22-222-20000000000000000000000002-2-220000
χ422-2-2-2-2222-2-222-222-22-2-22-222-2000000000000000000000000-222-20000
χ432-2-2-2-2222-2-222-222-2-222-22-2-22000000000000000000002-2-2200000000
χ442-2-2-2-2222-2-222-222-2-222-22-2-2200000000000000000000-222-200000000
χ45444-4-4-4-444i−4i4i−4i0000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ46444-4-4-4-444i−4i4i−4i000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ47444-4-4-4-44−4i4i−4i4i0000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ48444-4-4-4-44−4i4i−4i4i000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ494-4-444-4-444i−4i−4i4i0000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ504-4-444-4-444i−4i−4i4i000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ514-4-444-4-44−4i4i4i−4i0000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ524-4-444-4-44−4i4i4i−4i000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ5388-88-88-8-8000000000000000000000000000000000000000000000000
χ5488-8-88-88-8000000000000000000000000000000000000000000000000
χ558-888-8-88-8000000000000000000000000000000000000000000000000
χ568-88-888-8-8000000000000000000000000000000000000000000000000

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