Finite Group Databasebeta

← Group #116357

Character table — Group #116357

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222222222222222244444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
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
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911-1-1-1-11111-1-111111-1-1-1-11-1-11111-1-1-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ1011-1-1-1-11111-1-111111-1-1-1-11-1-11111-1-1-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ1111-1-1-1-11111-1-111111-1-1-1-11-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii
χ1211-1-1-1-11111-1-111111-1-1-1-11-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i
χ1311-1-1-1-11111-1-111111-1-1-1-11-1-1-1-1-1-1111111-1-1ii−i−iii−i−i-1-111−i−iii−i−iii
χ1411-1-1-1-11111-1-111111-1-1-1-11-1-1-1-1-1-1111111-1-1−i−iii−i−iii-1-111ii−i−iii−i−i
χ1511-1-1-1-11111-1-111111-1-1-1-11-1-1-1-1-1-11111-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ1611-1-1-1-11111-1-111111-1-1-1-11-1-1-1-1-1-11111-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ1722222222222222-2-2-22-2-2-2-22-200000000000000002-22-2000000000000
χ1822222222222222-2-2-22-2-2-2-22-20000000000000000-22-22000000000000
χ19222222222222-2-222-2-22-2-2-2-220000000000002-22-20000000000000000
χ20222222222222-2-222-2-22-2-2-2-22000000000000-22-220000000000000000
χ21222222222222-2-2-2-22-2-2222-2-2000000002-22-200000000000000000000
χ22222222222222-2-2-2-22-2-2222-2-200000000-22-2200000000000000000000
χ2322222222-2-2-2-22-22-22222-2-2-2-222-2-222-2-2000000000000000000000000
χ2422222222-2-2-2-22-22-22222-2-2-2-2-2-222-2-222000000000000000000000000
χ2522222222-2-2-2-22-2-22-22-2-222-2200000000000000000000000000002i−2i2i−2i
χ2622222222-2-2-2-22-2-22-22-2-222-220000000000000000000000000000−2i2i−2i2i
χ2722222222-2-2-2-2-222-2-2-22-2222-20000000000000000000000002i−2i2i−2i0000
χ2822222222-2-2-2-2-222-2-2-22-2222-2000000000000000000000000−2i2i−2i2i0000
χ2922222222-2-2-2-2-22-222-2-22-2-222000000000000000000002i−2i2i−2i00000000
χ3022222222-2-2-2-2-22-222-2-22-2-22200000000000000000000−2i2i−2i2i00000000
χ3122-2-2-2-22222-2-222-2-2-2-2222-2-2200000000000000002i−2i−2i2i000000000000
χ3222-2-2-2-22222-2-222-2-2-2-2222-2-220000000000000000−2i2i2i−2i000000000000
χ3322-2-2-2-22222-2-2-2-222-22-222-22-20000000000002i−2i−2i2i0000000000000000
χ3422-2-2-2-22222-2-2-2-222-22-222-22-2000000000000−2i2i2i−2i0000000000000000
χ3522-2-2-2-22222-2-2-2-2-2-2222-2-2222000000002-2-2200000000000000000000
χ3622-2-2-2-22222-2-2-2-2-2-2222-2-222200000000-222-200000000000000000000
χ3722-2-2-2-222-2-2222-22-22-2-2-22-22222-2-2-2-222000000000000000000000000
χ3822-2-2-2-222-2-2222-22-22-2-2-22-222-2-22222-2-2000000000000000000000000
χ3922-2-2-2-222-2-2222-2-22-2-222-222-200000000000000000000000000002-2-22
χ4022-2-2-2-222-2-2222-2-22-2-222-222-20000000000000000000000000000-222-2
χ4122-2-2-2-222-2-222-222-2-22-22-22-220000000000000000000000002-2-220000
χ4222-2-2-2-222-2-222-222-2-22-22-22-22000000000000000000000000-222-20000
χ4322-2-2-2-222-2-222-22-22222-22-2-2-2000000000000000000002i−2i−2i2i00000000
χ4422-2-2-2-222-2-222-22-22222-22-2-2-200000000000000000000−2i2i2i−2i00000000
χ454444-4-4-4-44-44-40000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ464444-4-4-4-44-44-4000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ474444-4-4-4-4-44-440000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ484444-4-4-4-4-44-44000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ4944-4-444-4-44-4-440000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5044-4-444-4-44-4-44000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5144-4-444-4-4-444-40000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ5244-4-444-4-4-444-4000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ538-88-88-88-8000000000000000000000000000000000000000000000000
χ548-88-8-88-88000000000000000000000000000000000000000000000000
χ558-8-888-8-88000000000000000000000000000000000000000000000000
χ568-8-88-888-8000000000000000000000000000000000000000000000000

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