Finite Group Databasebeta

← Group #148484

Character table — Group #148484

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11222222244444444444488888888161616161616161616161616161616161616161616161616
order12222444422222244444444444444224488888888888888888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111-1-1-1-11111-1-11-1-11-1-11111-1-1-1-11-11-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ1011111-1-1-1-11111-1-11-1-11-1-11111-1-1-1-11-11-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ1111111-1-1-1-11111-1-11-1-11-1-11111-1-1-1-1-11-11ii−i−i−i−iii-1-111ii−i−i−i−iii
χ1211111-1-1-1-11111-1-11-1-11-1-11111-1-1-1-1-11-11−i−iiiii−i−i-1-111−i−iiiii−i−i
χ1311111-1-1-1-11111-1-11-1-11-1-1-1-1-1-111111-11-1ii−i−iii−i−i-1-111−i−iii−i−iii
χ1411111-1-1-1-11111-1-11-1-11-1-1-1-1-1-111111-11-1−i−iii−i−iii-1-111ii−i−iii−i−i
χ1511111-1-1-1-11111-1-11-1-11-1-1-1-1-1-11111-11-11ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ1611111-1-1-1-11111-1-11-1-11-1-1-1-1-1-11111-11-11−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ1722222222222-2-2-2-2-22-2-22-200000000000000002-22-2000000000000
χ1822222222222-2-2-2-2-22-2-22-20000000000000000-22-22000000000000
χ19222222222-2-222-2-2-2-22-2-220000000000002-22-20000000000000000
χ20222222222-2-222-2-2-2-22-2-22000000000000-22-220000000000000000
χ21222222222-2-2-2-2222-2-22-2-20000000022-2-200000000000000000000
χ22222222222-2-2-2-2222-2-22-2-200000000-2-22200000000000000000000
χ2322222-2-2-2-222-2-222-2-22-2-2200000000000000002i−2i−2i2i000000000000
χ2422222-2-2-2-222-2-222-2-22-2-220000000000000000−2i2i2i−2i000000000000
χ2522222-2-2-2-2-2-22222-22-2-22-20000000000002i−2i−2i2i0000000000000000
χ2622222-2-2-2-2-2-22222-22-2-22-2000000000000−2i2i2i−2i0000000000000000
χ2722222-2-2-2-2-2-2-2-2-2-2222222000000002-2-2200000000000000000000
χ2822222-2-2-2-2-2-2-2-2-2-222222200000000-222-200000000000000000000
χ2922-22-222-2-22-22-22-222-2-2-22000000000000000000002i−2i2i−2i00000000
χ3022-22-222-2-22-22-22-222-2-2-2200000000000000000000−2i2i−2i2i00000000
χ3122-22-222-2-22-2-22-22-2222-2-20000000000000000000000002i−2i2i−2i0000
χ3222-22-222-2-22-2-22-22-2222-2-2000000000000000000000000−2i2i−2i2i0000
χ3322-22-222-2-2-222-2-22-2-2-222200000000000000000000000000002-22-2
χ3422-22-222-2-2-222-2-22-2-2-22220000000000000000000000000000-22-22
χ3522-22-222-2-2-22-222-22-22-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ3622-22-222-2-2-22-222-22-22-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ3722-22-2-2-2222-22-2-222-22-22-2000000000000000000002i−2i−2i2i00000000
χ3822-22-2-2-2222-22-2-222-22-22-200000000000000000000−2i2i2i−2i00000000
χ3922-22-2-2-2222-2-222-2-2-2-22220000000000000000000000002-2-220000
χ4022-22-2-2-2222-2-222-2-2-2-2222000000000000000000000000-222-20000
χ4122-22-2-2-222-222-22-2-2222-2-200000000000000000000000000002i−2i−2i2i
χ4222-22-2-2-222-222-22-2-2222-2-20000000000000000000000000000−2i2i2i−2i
χ4322-22-2-2-222-22-22-2222-2-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ4422-22-2-2-222-22-22-2222-2-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ45444-4-44-44-40000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ46444-4-44-44-4000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ47444-4-4-44-440000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ48444-4-4-44-44000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4944-4-444-4-440000000000002-2-222-2-22000000000000000000000000
χ5044-4-444-4-44000000000000-222-2-222-2000000000000000000000000
χ5144-4-44-444-40000000000002-2-22-222-2000000000000000000000000
χ5244-4-44-444-4000000000000-222-22-2-22000000000000000000000000
χ5316-16000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).