Finite Group Databasebeta

← Group #101243

Character table — Group #101243

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444422444444224444888888884444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ711111111111111111111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-11111
χ811111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−iii−i−i1-111-1-1ii−i−ii−ii−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−iii−i−i1-1-1-111−i−iiii−ii−i-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-11111-1-1−i−iii−i−iii1-111-1-1−i−iii−ii−ii11-1-1−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-11111-1-1−i−iii−i−iii1-1-1-111ii−i−i−ii−ii-1-111ii−i−i
χ1311111111-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii-1111-1-1ii−i−ii−i−ii-1-111−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii-11-1-111−i−iiii−i−ii11-1-1ii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i-1111-1-1−i−iii−iii−i-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i-11-1-111ii−i−i−iii−i11-1-1−i−iii
χ1722222222222222-2-2-2-2-2-200-2200222200000000000000-2-20000000000
χ1822222222222222-2-2-2-2-2-200-2200-2-2-2-200000000000000220000000000
χ19222222222222-2-22222-2-222-2-22200000000-2-200000000000000000000
χ20222222222222-2-22222-2-2-2-2-2-2-2-2000000002200000000000000000000
χ21222222222222-2-2-2-2-2-222002-20000002222000000000000-2-200000000
χ22222222222222-2-2-2-2-2-222002-2000000-2-2-2-20000000000002200000000
χ2322222222-2-2-2-22222-2-2-2-2002-20000002i2i−2i−2i000000000000−2i2i00000000
χ2422222222-2-2-2-22222-2-2-2-2002-2000000−2i−2i2i2i0000000000002i−2i00000000
χ2522222222-2-2-2-222-2-2222222-2-2-2-200000000-2200000000000000000000
χ2622222222-2-2-2-222-2-22222-2-2-2-222000000002-200000000000000000000
χ2722222222-2-2-2-2-2-222-2-22200-22002i2i−2i−2i00000000000000−2i2i0000000000
χ2822222222-2-2-2-2-2-222-2-22200-2200−2i−2i2i2i000000000000002i−2i0000000000
χ2922-22-2-22-22i2i−2i−2i002i−2i2-2002-2002i−2i000000000000001+i−1−i1−i−1+i000000001+i−1−i1−i−1+i
χ3022-22-2-22-22i2i−2i−2i002i−2i2-2002-2002i−2i00000000000000−1−i1+i−1+i1−i00000000−1−i1+i−1+i1−i
χ3122-22-2-22-22i2i−2i−2i002i−2i2-200-2200−2i2i000000000000001+i−1−i1−i−1+i00000000−1−i1+i−1+i1−i
χ3222-22-2-22-22i2i−2i−2i002i−2i2-200-2200−2i2i00000000000000−1−i1+i−1+i1−i000000001+i−1−i1−i−1+i
χ3322-22-2-22-2−2i−2i2i2i00−2i2i2-2002-200−2i2i000000000000001−i−1+i1+i−1−i000000001−i−1+i1+i−1−i
χ3422-22-2-22-2−2i−2i2i2i00−2i2i2-2002-200−2i2i00000000000000−1+i1−i−1−i1+i00000000−1+i1−i−1−i1+i
χ3522-22-2-22-2−2i−2i2i2i00−2i2i2-200-22002i−2i000000000000001−i−1+i1+i−1−i00000000−1+i1−i−1−i1+i
χ3622-22-2-22-2−2i−2i2i2i00−2i2i2-200-22002i−2i00000000000000−1+i1−i−1−i1+i000000001−i−1+i1+i−1−i
χ37444-4-4-4-4400000000004i−4i00000000002+2i−2−2i2−2i−2+2i0000000000000000000000
χ38444-4-4-4-4400000000004i−4i0000000000−2−2i2+2i−2+2i2−2i0000000000000000000000
χ39444-4-4-4-440000000000−4i4i00000000002−2i−2+2i2+2i−2−2i0000000000000000000000
χ40444-4-4-4-440000000000−4i4i0000000000−2+2i2−2i−2−2i2+2i0000000000000000000000
χ4144-44-4-44-44i4i−4i−4i00−4i4i-4400000000000000000000000000000000000000
χ4244-44-4-44-4−4i−4i4i4i004i−4i-4400000000000000000000000000000000000000
χ434-4444-4-4-400004-400000000000022−2222−2200000000000000000000000000
χ444-4444-4-4-400004-4000000000000−2222−222200000000000000000000000000
χ454-4444-4-4-40000-440000000000002i2−2i2−2i22i200000000000000000000000000
χ464-4444-4-4-40000-44000000000000−2i22i22i2−2i200000000000000000000000000
χ474-44-4-444-44i−4i4i−4i0000000000000000000000000000000000002-22i−2i0000
χ484-44-4-444-44i−4i4i−4i000000000000000000000000000000000000-22−2i2i0000
χ494-44-4-444-4−4i4i−4i4i0000000000000000000000000000000000002-2−2i2i0000
χ504-44-4-444-4−4i4i−4i4i000000000000000000000000000000000000-222i−2i0000
χ514-4-4-44-4444-4-440000000000000000000000002-22-20000000000000000
χ524-4-4-44-4444-4-44000000000000000000000000-22-220000000000000000
χ534-4-4-44-444-444-40000000000000000000000002-2-220000000000000000
χ544-4-4-44-444-444-4000000000000000000000000-222-20000000000000000
χ5588-8-888-8-8000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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