Finite Group Databasebeta

← Group #101424

Character table — Group #101424

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222224444448888888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i1-11-111-1-1i−ii−iii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i1-11-1-1-111i−ii−i−i−iii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i-11-1111-1-1−ii−iiii−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i-11-11-1-111−ii−ii−i−iii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-11-1−i−iii−i−iii1-11-111-1-1−ii−ii−i−iii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-11-1−i−iii−i−iii1-11-1-1-111−ii−iiii−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-11-1−i−iii−i−iii-11-1111-1-1i−ii−i−i−iii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-11-1−i−iii−i−iii-11-11-1-111i−ii−iii−i−i11-1-1−i−iii
χ17222222222222222222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ19222222222222-2-2-2-2-2-222-2-2-220000000022-2-200000000000000000000
χ20222222222222-2-2-2-2-2-222-2-2-2200000000-2-22200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2222-2000000000000000022-2-2000000000000
χ22222222222222-2-2-2-2-2-2-2-2222-20000000000000000-2-222000000000000
χ2322222222-2-2-2-22222-2-22222-2-2000000002-2-2200000000000000000000
χ2422222222-2-2-2-22222-2-22222-2-200000000-222-200000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-22200000000000000002i−2i−2i2i000000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2220000000000000000−2i2i2i−2i000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-222-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-222-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2922-2-222-2-222-2-2-2-2222-200000000002i−2i2i−2i0000000000000000i2−i2i2−i22−22−2
χ3022-2-222-2-222-2-2-2-2222-200000000002i−2i2i−2i0000000000000000−i2i2−i2i2−22−22
χ3122-2-222-2-222-2-2-2-2222-20000000000−2i2i−2i2i0000000000000000i2−i2i2−i2−22−22
χ3222-2-222-2-222-2-2-2-2222-20000000000−2i2i−2i2i0000000000000000−i2i2−i2i22−22−2
χ3322-2-222-2-2-2-22222-2-22-200000000002-2-220000000000000000i2−i2−i2i2−i2i2i2−i2
χ3422-2-222-2-2-2-22222-2-22-200000000002-2-220000000000000000−i2i2i2−i2i2−i2−i2i2
χ3522-2-222-2-2-2-22222-2-22-20000000000-222-20000000000000000i2−i2−i2i2i2−i2−i2i2
χ3622-2-222-2-2-2-22222-2-22-20000000000-222-20000000000000000−i2i2i2−i2−i2i2i2−i2
χ3744-4-444-4-444-4-444-4-4-4400000000000000000000000000000000000000
χ3844-4-444-4-4-4-444-4-444-4400000000000000000000000000000000000000
χ394-444-44-4-44-44-4000000000000000000000000000000002-22-200000000
χ404-444-44-4-44-44-400000000000000000000000000000000-22-2200000000
χ414-444-44-4-4-44-44000000000000000000000000000000002i−2i−2i2i00000000
χ424-444-44-4-4-44-4400000000000000000000000000000000−2i2i2i−2i00000000
χ434-44-44-44-400004i−4i4i−4i000000002+2i−2−2i2−2i−2+2i0000000000000000000000000000
χ444-44-44-44-400004i−4i4i−4i00000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000
χ454-44-44-44-40000−4i4i−4i4i000000002−2i−2+2i2+2i−2−2i0000000000000000000000000000
χ464-44-44-44-40000−4i4i−4i4i00000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000
χ474-4-444-4-4400004i−4i−4i4i004-44i−4i0000000000000000000000000000000000
χ484-4-444-4-4400004i−4i−4i4i00-44−4i4i0000000000000000000000000000000000
χ494-4-444-4-440000−4i4i4i−4i004-4−4i4i0000000000000000000000000000000000
χ504-4-444-4-440000−4i4i4i−4i00-444i−4i0000000000000000000000000000000000
χ514-4-4-4-44444-4-440000000000000000000000002-22-20000000000000000
χ524-4-4-4-44444-4-44000000000000000000000000-22-220000000000000000
χ534-4-4-4-4444-444-40000000000000000000000002-2-220000000000000000
χ544-4-4-4-4444-444-4000000000000000000000000-222-20000000000000000
χ55888-8-8-8-88000000000000000000000000000000000000000000000000
χ5688-88-8-88-8000000000000000000000000000000000000000000000000

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