Finite Group Databasebeta

← Group #500404

Character table — Group #500404

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122224444444444444888888888888888888888816161616161616161632323232
order12222244222244444444424444444444444444444442444444444488
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-111111111-1-111-1-1-1-1-11-11111-1-1-1-1
χ411111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-1-11111
χ5111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1
χ6111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-111
χ7111111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-111
χ8111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1111111-1-1
χ9111111-1-11111-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-11111-111-1-111-1-11-11-1
χ10111111-1-11111-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-11111-111-1-1-1-111-11-11
χ11111111-1-11111-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-11-1-1-1111-1-1-11-11
χ12111111-1-11111-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-11-1-1-11-1-1111-11-1
χ13111111-1-11111-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111-1-1-1-11-111-1-1-1111-1-11
χ14111111-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-11-111-111-1-1-111-1
χ15111111-1-11111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-11-111-1-111-111-1
χ16111111-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-11111-1-11-1-11
χ17222222222-2-222222222-2-2-2-20022000000000000-2-200000-2000000000
χ18222222222-2-22222-2-2-2-2-2-2-2-200-2-200000000000022000002000000000
χ1922222222-222-22-2-20000-2-2-222200220000000000000000-20-200000000
χ2022222222-222-22-2-20000-2-2-22-2-200-2-2000000000000000020200000000
χ2122222222-2-2-2-22-2-20000222-200000000000000220022-2-200000000000
χ2222222222-2-2-2-22-2-20000222-200000000000000-2-200-2-22200000000000
χ23222222-2-22-2-22-2-2-22222-2-22200-2-2000000000000-2-2000002000000000
χ24222222-2-22-2-22-2-2-2-2-2-2-2-2-22200220000000000002200000-2000000000
χ25222222-2-2-222-2-2220000-2-22-22200-2-20000000000000000-20200000000
χ26222222-2-2-222-2-2220000-2-22-2-2-20022000000000000000020-200000000
χ27222222-2-2-2-2-2-2-222000022-22000000000000002200-2-2-2200000000000
χ28222222-2-2-2-2-2-2-222000022-2200000000000000-2-200222-200000000000
χ2922-2-22-200-22-220002i2i−2i−2i2-20000000000002i2i−2i−2i002i−2i0000000002-20000
χ3022-2-22-200-22-220002i2i−2i−2i2-2000000000000−2i−2i2i2i002i−2i000000000-220000
χ3122-2-22-200-22-22000−2i−2i2i2i2-20000000000002i2i−2i−2i00−2i2i000000000-220000
χ3222-2-22-200-22-22000−2i−2i2i2i2-2000000000000−2i−2i2i2i00−2i2i0000000002-20000
χ3322-2-22-200-2-2220002i2i−2i−2i-22000000002i2i−2i−2i000000−2i2i00000002-2000000
χ3422-2-22-200-2-2220002i2i−2i−2i-2200000000−2i−2i2i2i000000−2i2i0000000-22000000
χ3522-2-22-200-2-222000−2i−2i2i2i-22000000002i2i−2i−2i0000002i−2i0000000-22000000
χ3622-2-22-200-2-222000−2i−2i2i2i-2200000000−2i−2i2i2i0000002i−2i00000002-2000000
χ374444-4-4440000-400000000000000002-22-22-22-20000000000000000000
χ384444-4-4440000-40000000000000000-22-22-22-220000000000000000000
χ394444-4-4-4-40000400000000000000002-22-2-22-220000000000000000000
χ404444-4-4-4-4000040000000000000000-22-222-22-20000000000000000000
χ4144-4-44-40044-4-40000000-4400000000000000000000000000000000000
χ4244-4-44-4004-44-400000004-400000000000000000000000000000000000
χ4344-4-4-4400000004-4000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000
χ4444-4-4-4400000004-400000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000
χ4544-4-4-440000000-44000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000
χ4644-4-4-440000000-4400000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000
χ474-44-4004i−4i00000002-22-200002i−2i2i−2i2-2000000002-2002i−2i0000000000000
χ484-44-4004i−4i00000002-22-20000−2i2i2i−2i-2200000000-2200−2i2i0000000000000
χ494-44-4004i−4i0000000-22-2200002i−2i−2i2i2-200000000-2200−2i2i0000000000000
χ504-44-4004i−4i0000000-22-220000−2i2i−2i2i-22000000002-2002i−2i0000000000000
χ514-44-400−4i4i00000002-22-200002i−2i−2i2i-2200000000-22002i−2i0000000000000
χ524-44-400−4i4i00000002-22-20000−2i2i−2i2i2-2000000002-200−2i2i0000000000000
χ534-44-400−4i4i0000000-22-2200002i−2i2i−2i-22000000002-200−2i2i0000000000000
χ544-44-400−4i4i0000000-22-220000−2i2i2i−2i2-200000000-22002i−2i0000000000000
χ558-8-88000000000004i−4i−4i4i0000000000000000000000000000000000000
χ568-8-8800000000000−4i4i4i−4i0000000000000000000000000000000000000

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