Finite Group Databasebeta

← Group #500054

Character table — Group #500054

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122224444444444444888888888888888888888816161616161616161632323232
order12222244222244444444422222444444444444444444444444444488
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111-1-1-1-111-1-1-1-1-11-11111-1-1-1-1
χ31111111111111111111111-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-1-11111
χ5111111111111-1-1-1-11111111111-1-1111111111-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1
χ6111111111111-1-1-1-11111111111-1-1-1-111111-1-111-1-11111-1-1-1-1-1-1-1-1-111
χ7111111111111-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11-111111-1-111
χ8111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1111111-1-1
χ9111111-1-111111111-1-1-111-111-1-1-1-111-111-1-1-1-11111-1-1-11-1-1111-1-11-11-1
χ10111111-1-111111111-1-1-111-111-1-1-1-1-1-1-111-1-111-1-111111-11-1-111-1-1-11-11
χ11111111-1-111111111-1-1-111-1-1-111-1-111-1-1-111-1-11111-1-1-11-1-11-1-111-11-11
χ12111111-1-111111111-1-1-111-1-1-111-1-1-1-1-1-1-11111-1-111111-11-1-1-1-1111-11-1
χ13111111-1-11111-1-1-1-1-1-1-111-111-1-11111-111-1-1-1-1-1-1-1-1111-1-111-1-1111-1-11
χ14111111-1-11111-1-1-1-1-1-1-111-111-1-111-1-1-111-1-11111-1-1-1-1-1111-1-1-111-111-1
χ15111111-1-11111-1-1-1-1-1-1-111-1-1-1111111-1-1-111-1-1-1-1-1-1111-1-11111-1-1-111-1
χ16111111-1-11111-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1111111-1-1-1-1-1111-111-1-11-1-11
χ17222222222-2-222222222-2-2-200002200-200000000-2-200000-2000000000
χ18222222222-2-22-2-2-2-2222-2-2-20000-2-200-20000000022000002000000000
χ1922222222-222-200002-2-2-2-2-200000022200002200000000-20-200000000
χ2022222222-222-200002-2-2-2-2-2000000-2-220000-2-20000000020200000000
χ2122222222-2-2-2-200002-2-222200000000-2000000220022-2-200000000000
χ2222222222-2-2-2-200002-2-222200000000-2000000-2-200-2-22200000000000
χ23222222-2-22-2-222222-2-2-2-2-220000-2-200200000000-2-2000002000000000
χ24222222-2-22-2-22-2-2-2-2-2-2-2-2-22000022002000000002200000-2000000000
χ25222222-2-2-222-20000-222-2-2200000022-20000-2-20000000020-200000000
χ26222222-2-2-222-20000-222-2-22000000-2-2-200002200000000-20200000000
χ27222222-2-2-2-2-2-20000-22222-20000000020000002200-2-22-200000000000
χ28222222-2-2-2-2-2-20000-22222-2000000002000000-2-20022-2200000000000
χ292-2-222-20022-2-22i2i−2i−2i0002-20002-200000002-200002i−2i0000000002i−2i0000
χ302-2-222-20022-2-22i2i−2i−2i0002-2000-220000000-2200002i−2i000000000−2i2i0000
χ312-2-222-20022-2-2−2i−2i2i2i0002-20002-200000002-20000−2i2i000000000−2i2i0000
χ322-2-222-20022-2-2−2i−2i2i2i0002-2000-220000000-220000−2i2i0000000002i−2i0000
χ332-2-222-2002-22-22i2i−2i−2i000-2202-200000002-2000000−2i2i00000002i−2i000000
χ342-2-222-2002-22-22i2i−2i−2i000-220-220000000-22000000−2i2i0000000−2i2i000000
χ352-2-222-2002-22-2−2i−2i2i2i000-2202-200000002-20000002i−2i0000000−2i2i000000
χ362-2-222-2002-22-2−2i−2i2i2i000-220-220000000-220000002i−2i00000002i−2i000000
χ374444-4-44400000000-40000022-2-200000-2-222000000000000000000000
χ384444-4-44400000000-400000-2-2220000022-2-2000000000000000000000
χ394444-4-4-4-400000000400000222200000-2-2-2-2000000000000000000000
χ404444-4-4-4-400000000400000-2-2-2-2000002222000000000000000000000
χ414-44-4004i−4i00002i−2i2i−2i00000000002-22-2000002i−2i2i−2i002-20000000000000
χ424-44-4004i−4i00002i−2i2i−2i00000000002-2-2200000−2i2i−2i2i00-220000000000000
χ434-44-4004i−4i0000−2i2i−2i2i0000000000-222-2000002i−2i−2i2i00-220000000000000
χ444-44-4004i−4i0000−2i2i−2i2i0000000000-22-2200000−2i2i2i−2i002-20000000000000
χ454-44-400−4i4i00002i−2i2i−2i0000000000-222-200000−2i2i2i−2i00-220000000000000
χ464-44-400−4i4i00002i−2i2i−2i0000000000-22-22000002i−2i−2i2i002-20000000000000
χ474-44-400−4i4i0000−2i2i−2i2i00000000002-22-200000−2i2i−2i2i002-20000000000000
χ484-44-400−4i4i0000−2i2i−2i2i00000000002-2-22000002i−2i2i−2i00-220000000000000
χ494-4-444-400-44-440000000-4400000000000000000000000000000000000
χ504-4-444-400-4-44400000004-400000000000000000000000000000000000
χ514-4-44-44000000000004-40002-22-200000-22-22000000000000000000000
χ524-4-44-44000000000004-4000-22-22000002-22-2000000000000000000000
χ534-4-44-4400000000000-440002-2-2200000-222-2000000000000000000000
χ544-4-44-4400000000000-44000-222-2000002-2-22000000000000000000000
χ5588-8-8000000004-4-440000000000000000000000000000000000000000
χ5688-8-800000000-444-40000000000000000000000000000000000000000

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