Finite Group Databasebeta

← Group #100748

Character table — Group #100748

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444448888888888888888888888888881616161616161616161616163232
order12222222444444444444444444444888888888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1
χ911111111-1-1-1-11-1-11-1-1-111111-1-11-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-11-1-11-1-1-111111-1-11-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-1-111-11
χ1111111111-1-1-1-11-1-11-1-1-111111-1-11-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-1-111-11
χ1211111111-1-1-1-11-1-11-1-1-111111-1-11-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-11-1
χ1311111111-1-1-1-11-1-11-1-1-11-1-1-1-111111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii11-1-1-11
χ1411111111-1-1-1-11-1-11-1-1-11-1-1-1-111111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1-1-11-1-11-1-1-11-1-1-1-111111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-11-1-11-1-1-11-1-1-1-111111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-11
χ172222222222222-2-22-2-22-222-2-222-2-2-2000000000000000000000000000000
χ182222222222222-2-22-2-22-2-2-222-2-2-222000000000000000000000000000000
χ19222222222222-22-2-22-2-22000000-200000022220000-2-2-2-200000000000000
χ20222222222222-22-2-22-2-22000000-2000000-2-2-2-20000222200000000000000
χ21222222222222-2-22-2-22-2-200000020022220000-2-2-2-2000000000000000000
χ22222222222222-2-22-2-22-2-2000000200-2-2-2-200002222000000000000000000
χ2322222222-2-2-2-2222222-2-222-2-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2-2222222-2-2-2-22222-2-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-22-2-22-22-20000002002i2i−2i−2i0000−2i−2i2i2i000000000000000000
χ2622222222-2-2-2-2-22-2-22-22-2000000200−2i−2i2i2i00002i2i−2i−2i000000000000000000
χ2722222222-2-2-2-2-2-22-2-2222000000-20000002i2i−2i−2i0000−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-22-2-2222000000-2000000−2i−2i2i2i00002i2i−2i−2i00000000000000
χ2922-2-222-2-20000222-2-2-200002-22-20002−22−22−22−22−22−22−22−200000000000000
χ3022-2-222-2-20000222-2-2-200002-22-2000−22−22−22−22−22−22−22−2200000000000000
χ3122-2-222-2-20000222-2-2-20000-22-220002−22−2−22−222−22−2−22−2200000000000000
χ3222-2-222-2-20000222-2-2-20000-22-22000−22−222−22−2−22−222−22−200000000000000
χ3322-2-222-2-200002-2-2-22200002-2-22000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000
χ3422-2-222-2-200002-2-2-22200002-2-22000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000
χ3522-2-222-2-200002-2-2-2220000-222-2000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000000000
χ3622-2-222-2-200002-2-2-2220000-222-2000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000000000
χ3722-2-222-2-20000-22-22-22002i−2i000002i−2ii2−i2−i2i22−22−2−i2i2i2−i2−22−2200000000000000
χ3822-2-222-2-20000-22-22-22002i−2i000002i−2i−i2i2i2−i2−22−22i2−i2−i2i22−22−200000000000000
χ3922-2-222-2-20000-22-22-2200−2i2i00000−2i2ii2−i2−i2i2−22−22−i2i2i2−i22−22−200000000000000
χ4022-2-222-2-20000-22-22-2200−2i2i00000−2i2i−i2i2i2−i22−22−2i2−i2−i2i2−22−2200000000000000
χ4122-2-222-2-20000-2-2222-2002i−2i00000−2i2i2−22−2−i2i2i2−i2−22−22i2−i2−i2i200000000000000
χ4222-2-222-2-20000-2-2222-2002i−2i00000−2i2i−22−22i2−i2−i2i22−22−2−i2i2i2−i200000000000000
χ4322-2-222-2-20000-2-2222-200−2i2i000002i−2i2−22−2i2−i2−i2i2−22−22−i2i2i2−i200000000000000
χ4422-2-222-2-20000-2-2222-200−2i2i000002i−2i−22−22−i2i2i2−i22−22−2i2−i2−i2i200000000000000
χ454444-4-4-4-44-4-44000000000000000000000000000000000000000002-22-200
χ464444-4-4-4-44-4-4400000000000000000000000000000000000000000-22-2200
χ474444-4-4-4-4-444-4000000000000000000000000000000000000000002-2-2200
χ484444-4-4-4-4-444-400000000000000000000000000000000000000000-222-200
χ494-44-44-44-444-4-40000000000000000000000000000000002-22-20000000000
χ504-44-44-44-444-4-4000000000000000000000000000000000-22-220000000000
χ514-44-44-44-4-4-4440000000000000000000000000000000002i−2i−2i2i0000000000
χ524-44-44-44-4-4-444000000000000000000000000000000000−2i2i2i−2i0000000000
χ534-44-4-44-444-44-400000000000000000000000000000000000002i−2i2i−2i000000
χ544-44-4-44-444-44-40000000000000000000000000000000000000−2i2i−2i2i000000
χ554-44-4-44-44-44-4400000000000000000000000000000000000002-2-22000000
χ564-44-4-44-44-44-440000000000000000000000000000000000000-222-2000000
χ5788-8-8-8-888000000000000000000000000000000000000000000000000000
χ588-8-888-8-88000000000000000000000000000000000000000000000000000
χ598-8-88-888-8000000000000000000000000000000000000000000000000000

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