Finite Group Databasebeta

← Group #253333

Character table — Group #253333

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122224444444444444888888888888888888888816161616161616161632323232
order12222244224444444444422444444444444888888882244444448888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1
χ3111111111111111111111-1-111-1-1-1-11111-1-11111111111-1-111-11-1-1-1-1-1
χ4111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111
χ51111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1111-1-1
χ61111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-11-1-111
χ71111111111111-1-1-1-11111-1-111-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-1-111
χ81111111111111-1-1-1-11111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-111-1-1
χ911111111-1-11-1-11111111111-1-1111111-1-1111111-1-1-1-11-1-1-11-1-1-1-11-11-1
χ1011111111-1-11-1-11111111111-1-1111111-1-111-1-1-1-11111-11-1-1-11-1-1-1-11-11
χ1111111111-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1111-11-11-11-11
χ1211111111-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1111-111-111-11-1
χ1311111111-1-11-1-1-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1-1-1-1111-11-11-11-1-11
χ1411111111-1-11-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-111111-1111-1-11-1-111-1
χ1511111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-11-1-1-11111-111-1
χ1611111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111111-1-1-11-11111-1-11
χ1722222222222222222-2-2-2-200-2-20000-2-22200000000000000000-200000
χ182222222222222-2-2-2-2-2-2-2-200-2-2000022-2-200000000000000000200000
χ1922222222-2-22-2-22222-2-2-2-200220000-2-2-2-200000000000000000200000
χ2022222222-2-22-2-2-2-2-2-2-2-2-2-200220000222200000000000000000-200000
χ21222222-2-222-2-2-2000022-2-2002-200220000-2-200000000002-2000000000
χ22222222-2-222-2-2-2000022-2-2002-200-2-20000220000000000-22000000000
χ23222222-2-222-2-2-20000-2-22222-22-2-20000000000000000000000-2020000
χ24222222-2-222-2-2-20000-2-222-2-2-2222000000000000000000000020-20000
χ25222222-2-2-2-2-222000022-2-200-2200220000-2-20000000000-22000000000
χ26222222-2-2-2-2-222000022-2-200-2200-2-200002200000000002-2000000000
χ27222222-2-2-2-2-2220000-2-222222-2-2-2000000000000000000000020-20000
χ28222222-2-2-2-2-2220000-2-222-2-22-2220000000000000000000000-2020000
χ292222-2-2-2-2002002i2i−2i−2i2-22-2000000002i−2i000000002i2i−2i−2i02000-20000000
χ302222-2-2-2-2002002i2i−2i−2i2-22-2000000002i−2i00000000−2i−2i2i2i0-200020000000
χ312222-2-2-2-2002002i2i−2i−2i-22-2200000000−2i2i00002i2i−2i−2i00002000-200000000
χ322222-2-2-2-2002002i2i−2i−2i-22-2200000000−2i2i0000−2i−2i2i2i0000-2000200000000
χ332222-2-2-2-200200−2i−2i2i2i2-22-200000000−2i2i000000002i2i−2i−2i0-200020000000
χ342222-2-2-2-200200−2i−2i2i2i2-22-200000000−2i2i00000000−2i−2i2i2i02000-20000000
χ352222-2-2-2-200200−2i−2i2i2i-22-22000000002i−2i00002i2i−2i−2i0000-2000200000000
χ362222-2-2-2-200200−2i−2i2i2i-22-22000000002i−2i0000−2i−2i2i2i00002000-200000000
χ374444-4-44400-40000004-4-4400000000000000000000000000000000000
χ384444-4-44400-4000000-444-400000000000000000000000000000000000
χ3944-4-4004i−4i000002+2i−2−2i2−2i−2+2i00002-2002i−2i2-200002i−2i000000000000000000000
χ4044-4-4004i−4i000002+2i−2−2i2−2i−2+2i0000-2200−2i2i-220000−2i2i000000000000000000000
χ4144-4-4004i−4i00000−2−2i2+2i−2+2i2−2i00002-2002i−2i-220000−2i2i000000000000000000000
χ4244-4-4004i−4i00000−2−2i2+2i−2+2i2−2i0000-2200−2i2i2-200002i−2i000000000000000000000
χ4344-4-400−4i4i000002−2i−2+2i2+2i−2−2i00002-200−2i2i2-20000−2i2i000000000000000000000
χ4444-4-400−4i4i000002−2i−2+2i2+2i−2−2i0000-22002i−2i-2200002i−2i000000000000000000000
χ4544-4-400−4i4i00000−2+2i2−2i−2−2i2+2i00002-200−2i2i-2200002i−2i000000000000000000000
χ4644-4-400−4i4i00000−2+2i2−2i−2−2i2+2i0000-22002i−2i2-20000−2i2i000000000000000000000
χ474-4-444-4000004-400000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000
χ484-4-444-4000004-40000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000
χ494-4-444-400000-4400000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000
χ504-4-444-400000-440000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000
χ514-4-44-44004-400000000000000000000000002-2-222-2-220000000000000
χ524-4-44-44004-40000000000000000000000000-222-2-222-20000000000000
χ534-4-44-4400-4400000000000000000000000002-2-22-222-20000000000000
χ544-4-44-4400-440000000000000000000000000-222-22-2-220000000000000
χ558-88-80000000000000000000000000004i−4i00000000000000000000000
χ568-88-8000000000000000000000000000−4i4i00000000000000000000000

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