Finite Group Databasebeta

← Group #101341

Character table — Group #101341

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444444444888888882224448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-111-11111-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-1-1-11111-111-111-1-111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ911111111-1-1-1-11-1-1-1-1-11-11111-1-1ii−i−iii−i−i111-1-1-1i−ii−iii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-11-1-1-1-1-11-11111-1-1ii−i−iii−i−i1-1-1-111i−ii−i−i−iii-1-111−i−iii
χ1111111111-1-1-1-11-1-1-1-1-11-11111-1-1−i−iii−i−iii111-1-1-1−ii−ii−i−iii11-1-1−i−iii
χ1211111111-1-1-1-11-1-1-1-1-11-11111-1-1−i−iii−i−iii1-1-1-111−ii−iiii−i−i-1-111ii−i−i
χ1311111111-1-1-1-11-1-1-1-1-11-111-1-111ii−i−i−i−iii-1111-1-1i−i−iiii−i−i-1-111−i−iii
χ1411111111-1-1-1-11-1-1-1-1-11-111-1-111ii−i−i−i−iii-1-1-1111i−i−ii−i−iii11-1-1ii−i−i
χ1511111111-1-1-1-11-1-1-1-1-11-111-1-111−i−iiiii−i−i-1111-1-1−iii−i−i−iii-1-111ii−i−i
χ1611111111-1-1-1-11-1-1-1-1-11-111-1-111−i−iiiii−i−i-1-1-1111−iii−iii−i−i11-1-1−i−iii
χ172222222222222-222-2-22-2-2-2222200000000-200-2000000000000000000
χ182222222222222-222-2-22-2-2-2-2-2-2-2000000002002000000000000000000
χ19222222222222-22-2-2-2-2-222-200000000222200000000-2-2000000000000
χ20222222222222-22-2-2-2-2-222-200000000-2-2-2-20000000022000000000000
χ21222222222222-2-2-2-222-2-2-22000022220000000000-2-200000000000000
χ22222222222222-2-2-2-222-2-2-220000-2-2-2-200000000002200000000000000
χ2322222222-2-2-2-222-2-22222-2-222-2-200000000-2002000000000000000000
χ2422222222-2-2-2-222-2-22222-2-2-2-22200000000200-2000000000000000000
χ2522222222-2-2-2-2-2222-2-2-22-2200002i2i−2i−2i0000000000−2i2i00000000000000
χ2622222222-2-2-2-2-2222-2-2-22-220000−2i−2i2i2i00000000002i−2i00000000000000
χ2722222222-2-2-2-2-2-22222-2-22-2000000002i2i−2i−2i00000000−2i2i000000000000
χ2822222222-2-2-2-2-2-22222-2-22-200000000−2i−2i2i2i000000002i−2i000000000000
χ2922-2-22-2-2222-2-2202-200-20002i−2i2i−2i0000000000000000002−22−20000i2−i2i2−i2
χ3022-2-22-2-2222-2-2202-200-20002i−2i2i−2i000000000000000000−22−220000−i2i2−i2i2
χ3122-2-22-2-2222-2-2202-200-2000−2i2i−2i2i0000000000000000002−22−20000−i2i2−i2i2
χ3222-2-22-2-2222-2-2202-200-2000−2i2i−2i2i000000000000000000−22−220000i2−i2i2−i2
χ3322-2-22-2-22-2-22220-2200-20002i−2i−2i2i000000000000000000i2−i2−i2i20000−222−2
χ3422-2-22-2-22-2-22220-2200-20002i−2i−2i2i000000000000000000−i2i2i2−i200002−2−22
χ3522-2-22-2-22-2-22220-2200-2000−2i2i2i−2i000000000000000000i2−i2−i2i200002−2−22
χ3622-2-22-2-22-2-22220-2200-2000−2i2i2i−2i000000000000000000−i2i2i2−i20000−222−2
χ37444-4-44-4-44i−4i4i−4i0000000000000000000000000000000000002-22i−2i0000
χ38444-4-44-4-44i−4i4i−4i000000000000000000000000000000000000-22−2i2i0000
χ39444-4-44-4-4−4i4i−4i4i0000000000000000000000000000000000002-2−2i2i0000
χ40444-4-44-4-4−4i4i−4i4i000000000000000000000000000000000000-222i−2i0000
χ4144-44-4-44-44i−4i−4i4i000000000000000000000002-202i−2i0000000000000000
χ4244-44-4-44-44i−4i−4i4i00000000000000000000000-220−2i2i0000000000000000
χ4344-44-4-44-4−4i4i4i−4i000000000000000000000002-20−2i2i0000000000000000
χ4444-44-4-44-4−4i4i4i−4i00000000000000000000000-2202i−2i0000000000000000
χ4544-4-44-4-4444-4-4-40-440040000000000000000000000000000000000000
χ4644-4-44-4-44-4-444-404-40040000000000000000000000000000000000000
χ474-4444-4-4-4000000004i−4i000000002+2i−2−2i2−2i−2+2i00000000000000000000000000
χ484-4444-4-4-4000000004i−4i00000000−2−2i2+2i−2+2i2−2i00000000000000000000000000
χ494-4444-4-4-400000000−4i4i000000002−2i−2+2i2+2i−2−2i00000000000000000000000000
χ504-4444-4-4-400000000−4i4i00000000−2+2i2−2i−2−2i2+2i00000000000000000000000000
χ514-44-4-4-44400000400000-400000000002i2−2i22i2−2i20000000000000000000000
χ524-44-4-4-44400000400000-40000000000−2i22i2−2i22i20000000000000000000000
χ534-44-4-4-44400000-4000004000000000022−22−22220000000000000000000000
χ544-44-4-4-44400000-40000040000000000−222222−220000000000000000000000
χ558-8-88-88-88000000000000000000000000000000000000000000000000
χ568-8-8-8888-8000000000000000000000000000000000000000000000000

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