Finite Group Databasebeta

← Group #101310

Character table — Group #101310

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444444444888888884444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-11-1-11111-1-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ7111111111111111111111-1-11-1-1-1-1-1-11111-111-111-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−iii−i−i-1111-1-1i−ii−i11-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−iii−i−i-1-1-1111i−ii−i-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-11111-1-1−i−iii−i−iii-1111-1-1−ii−ii11-1-1−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-11111-1-1−i−iii−i−iii-1-1-1111−ii−ii-1-111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111-1-11-1-1111ii−i−i−i−iii111-1-1-1i−i−ii-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-11-1-1111ii−i−i−i−iii1-1-1-111i−i−ii11-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-11-1-1111−i−iiiii−i−i111-1-1-1−iii−i-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111-1-11-1-1111−i−iiiii−i−i1-1-1-111−iii−i11-1-1ii−i−i−i−iii
χ1722222222222222-2-222-2-2-222-22200000000-200-2000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2000000002002000000000000000000
χ19222222222222-2-22-2-2-22-2200-2000000222200000000-2-2000000000000
χ20222222222222-2-22-2-2-22-2200-2000000-2-2-2-20000000022000000000000
χ21222222222222-2-2-22-2-2-22-20020022220000000000-2-200000000000000
χ22222222222222-2-2-22-2-2-22-200200-2-2-2-200000000002200000000000000
χ2322222222-2-2-2-2222-2-2-22-2-2002002i2i−2i−2i0000000000−2i2i00000000000000
χ2422222222-2-2-2-2222-2-2-22-2-200200−2i−2i2i2i00000000002i−2i00000000000000
χ2522222222-2-2-2-222-22-2-2-22200-20000002i2i−2i−2i00000000−2i2i000000000000
χ2622222222-2-2-2-222-22-2-2-22200-2000000−2i−2i2i2i000000002i−2i000000000000
χ2722222222-2-2-2-2-2-2222222-222-2-2-200000000200-2000000000000000000
χ2822222222-2-2-2-2-2-2222222-2-2-2-22200000000-2002000000000000000000
χ2922-2-2-222-22i2i−2i−2i2i−2i002-20002-202i−2i00000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ3022-2-2-222-22i2i−2i−2i2i−2i002-20002-202i−2i0000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ3122-2-2-222-22i2i−2i−2i2i−2i002-2000-220−2i2i00000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ3222-2-2-222-22i2i−2i−2i2i−2i002-2000-220−2i2i0000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ3322-2-2-222-2−2i−2i2i2i−2i2i002-20002-20−2i2i00000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ3422-2-2-222-2−2i−2i2i2i−2i2i002-20002-20−2i2i0000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ3522-2-2-222-2−2i−2i2i2i−2i2i002-2000-2202i−2i00000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ3622-2-2-222-2−2i−2i2i2i−2i2i002-2000-2202i−2i0000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ374444-4-4-4-44-44-4000000000000000000000000000000002-22-200000000
χ384444-4-4-4-44-44-400000000000000000000000000000000-22-2200000000
χ394444-4-4-4-4-44-44000000000000000000000000000000002-2-2200000000
χ404444-4-4-4-4-44-4400000000000000000000000000000000-222-200000000
χ4144-4-44-4-444i−4i−4i4i000000000000000000000002i−2i02-20000000000000000
χ4244-4-44-4-444i−4i−4i4i00000000000000000000000−2i2i0-220000000000000000
χ4344-4-44-4-44−4i4i4i−4i000000000000000000000002i−2i0-220000000000000000
χ4444-4-44-4-44−4i4i4i−4i00000000000000000000000−2i2i02-20000000000000000
χ4544-4-4-444-44i4i−4i−4i−4i4i00-4400000000000000000000000000000000000000
χ4644-4-4-444-4−4i−4i4i4i4i−4i00-4400000000000000000000000000000000000000
χ474-44-444-4-400000004000-400000022−2222−2200000000000000000000000000
χ484-44-444-4-400000004000-4000000−2222−222200000000000000000000000000
χ494-44-444-4-40000000-400040000002i2−2i2−2i22i200000000000000000000000000
χ504-44-444-4-40000000-40004000000−2i22i22i2−2i200000000000000000000000000
χ514-44-4-4-4440000004000-4000000000002i2−2i22i2−2i20000000000000000000000
χ524-44-4-4-4440000004000-400000000000−2i22i2−2i22i20000000000000000000000
χ534-44-4-4-444000000-400040000000000022−22−22220000000000000000000000
χ544-44-4-4-444000000-4000400000000000−222222−220000000000000000000000
χ558-8-888-88-8000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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