Finite Group Databasebeta

← Group #100752

Character table — Group #100752

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
χ5111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1
χ911111111-1-1-1-11-1-11-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-11-1-11-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-1-111-11
χ1111111111-1-1-1-11-1-11-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-1-111-11
χ1211111111-1-1-1-11-1-11-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-11-1
χ1311111111-1-1-1-11-1-11-1-1-111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii11-1-1-11
χ1411111111-1-1-1-11-1-11-1-1-111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1-1-11-1-11-1-1-111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-11-1-11-1-1-111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-11
χ172222222222222-2-22-2-22-2-222-2-222-2-2000000000000000000000000000000
χ182222222222222-2-22-2-22-2-2-2-222-2-222000000000000000000000000000000
χ19222222222222-22-2-22-2-22-200000000000022220000-2-2-2-200000000000000
χ20222222222222-22-2-22-2-22-2000000000000-2-2-2-20000222200000000000000
χ21222222222222-2-22-2-22-2-220000000022220000-2-2-2-2000000000000000000
χ22222222222222-2-22-2-22-2-2200000000-2-2-2-200002222000000000000000000
χ2322222222-2-2-2-2222222-2-2-222-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2-2222222-2-2-2-2-22222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-22-2-22-22-22000000002i2i−2i−2i0000−2i−2i2i2i000000000000000000
χ2622222222-2-2-2-2-22-2-22-22-2200000000−2i−2i2i2i00002i2i−2i−2i000000000000000000
χ2722222222-2-2-2-2-2-22-2-2222-20000000000002i2i−2i−2i0000−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-22-2-2222-2000000000000−2i−2i2i2i00002i2i−2i−2i00000000000000
χ2922-222-2-2-20000222-2-2-2000002-22-2002−22−22−22−22−22−22−22−200000000000000
χ3022-222-2-2-20000222-2-2-2000002-22-200−22−22−22−22−22−22−22−2200000000000000
χ3122-222-2-2-20000222-2-2-200000-22-22002−22−2−22−222−22−2−22−2200000000000000
χ3222-222-2-2-20000222-2-2-200000-22-2200−22−222−22−2−22−222−22−200000000000000
χ3322-222-2-2-200002-2-2-222000002-2-2200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000
χ3422-222-2-2-200002-2-2-222000002-2-2200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000
χ3522-222-2-2-200002-2-2-22200000-222-200i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000000000
χ3622-222-2-2-200002-2-2-22200000-222-200−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000000000
χ3722-222-2-2-20000-22-22-220002i−2i00002i−2ii2−i2−i2i22−22−2−i2i2i2−i2−22−2200000000000000
χ3822-222-2-2-20000-22-22-220002i−2i00002i−2i−i2i2i2−i2−22−22i2−i2−i2i22−22−200000000000000
χ3922-222-2-2-20000-22-22-22000−2i2i0000−2i2ii2−i2−i2i2−22−22−i2i2i2−i22−22−200000000000000
χ4022-222-2-2-20000-22-22-22000−2i2i0000−2i2i−i2i2i2−i22−22−2i2−i2−i2i2−22−2200000000000000
χ4122-222-2-2-20000-2-2222-20002i−2i0000−2i2i2−22−2−i2i2i2−i2−22−22i2−i2−i2i200000000000000
χ4222-222-2-2-20000-2-2222-20002i−2i0000−2i2i−22−22i2−i2−i2i22−22−2−i2i2i2−i200000000000000
χ4322-222-2-2-20000-2-2222-2000−2i2i00002i−2i2−22−2i2−i2−i2i2−22−22−i2i2i2−i200000000000000
χ4422-222-2-2-20000-2-2222-2000−2i2i00002i−2i−22−22−i2i2i2−i22−22−2i2−i2−i2i200000000000000
χ45444-4-4-4-444-4-44000000000000000000000000000000000000000002i−2i2i−2i00
χ46444-4-4-4-444-4-4400000000000000000000000000000000000000000−2i2i−2i2i00
χ47444-4-4-4-44-444-4000000000000000000000000000000000000000002i−2i−2i2i00
χ48444-4-4-4-44-444-400000000000000000000000000000000000000000−2i2i2i−2i00
χ494-4-44-44-4444-4-40000000000000000000000000000000002i−2i2i−2i0000000000
χ504-4-44-44-4444-4-4000000000000000000000000000000000−2i2i−2i2i0000000000
χ514-4-44-44-44-4-4440000000000000000000000000000000002-2-220000000000
χ524-4-44-44-44-4-444000000000000000000000000000000000-222-20000000000
χ534-4-4-44-4444-44-400000000000000000000000000000000000002i−2i2i−2i000000
χ544-4-4-44-4444-44-40000000000000000000000000000000000000−2i2i−2i2i000000
χ554-4-4-44-444-44-4400000000000000000000000000000000000002-2-22000000
χ564-4-4-44-444-44-440000000000000000000000000000000000000-222-2000000
χ5788-8-8-888-8000000000000000000000000000000000000000000000000000
χ588-888-8-88-8000000000000000000000000000000000000000000000000000
χ598-88-888-8-8000000000000000000000000000000000000000000000000000

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