Finite Group Databasebeta

← Group #500520

Character table — Group #500520

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122224444444444444888888888888888888888816161616161616161632323232
order12222244444444444444422444444444444444444442444488888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1
χ3111111111111111111111-1-111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-11111111111-1-11111-1-11111-1-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-11111-1-1-111-1-1-1-1-1-111
χ71111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-111
χ81111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111111-1-1
χ9111111-1-1-1-111-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1-11-11-111-1-11-11-1
χ10111111-1-1-1-111-11111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-11-1111-1-1-11-11
χ11111111-1-1-1-111-111111111-1-1-1-11111-1-111-1-111-1-111-1-1-11-11-1-1-111-11-11
χ12111111-1-1-1-111-111111111-1-1-1-11111-1-111-1-1-1-111-1-111-1-11-11-1-1111-11-1
χ13111111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11-1-1111-1-11
χ14111111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11111-1-11-111-1-1-111-111-1
χ15111111-1-1-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1111-1-1-111-1
χ16111111-1-1-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-11-111-111-1-11-1-11
χ172222222222-2-22222222-2-200-2-200-2-200002200000000-2000000000000
χ182222222222-2-22-2-2-2-222-2-200-2-200220000-2-2000000002000000000000
χ1922222222-2-22-220000-2-22-2002-2000000000000002222000-2-200000000
χ2022222222-2-22-220000-2-22-2002-200000000000000-2-2-2-20002200000000
χ2122222222-2-2-2220000-2-2-2200-220000000000222200000-2-20000000000
χ2222222222-2-2-2220000-2-2-2200-220000000000-2-2-2-200000220000000000
χ23222222-2-2222-2-20000-2-22-200-220000000000000022-2-2000-2200000000
χ24222222-2-2222-2-20000-2-22-200-2200000000000000-2-2220002-200000000
χ25222222-2-222-22-20000-2-2-22002-2000000000022-2-200000-220000000000
χ26222222-2-222-22-20000-2-2-22002-20000000000-2-222000002-20000000000
χ27222222-2-2-2-2-2-2-2222222-2-2002200-2-20000-2-2000000002000000000000
χ28222222-2-2-2-2-2-2-2-2-2-2-222-2-20022002200002200000000-2000000000000
χ292-22-22-200002-202i2i−2i−2i2-2-2200002i−2i2i−2i002i−2i000000000000000002-20000
χ302-22-22-200002-202i2i−2i−2i2-2-220000−2i2i2i−2i00−2i2i00000000000000000-220000
χ312-22-22-200002-20−2i−2i2i2i2-2-2200002i−2i−2i2i002i−2i00000000000000000-220000
χ322-22-22-200002-20−2i−2i2i2i2-2-220000−2i2i−2i2i00−2i2i000000000000000002-20000
χ332-22-22-20000-2202i2i−2i−2i2-22-22-20000−2i2i2-2000000000000000002i−2i000000
χ342-22-22-20000-2202i2i−2i−2i2-22-2-220000−2i2i-2200000000000000000−2i2i000000
χ352-22-22-20000-220−2i−2i2i2i2-22-22-200002i−2i2-200000000000000000−2i2i000000
χ362-22-22-20000-220−2i−2i2i2i2-22-2-2200002i−2i-22000000000000000002i−2i000000
χ374444-4-4440000-4000000002200-2-200-2-22200000000000000000000000
χ384444-4-4440000-400000000-2-200220022-2-200000000000000000000000
χ394444-4-4-4-4000040000000022002200-2-2-2-200000000000000000000000
χ404444-4-4-4-40000400000000-2-200-2-200222200000000000000000000000
χ414-44-44-400004400000-44-4-400000000000000000000000000000000000
χ424-44-44-40000-4-400000-444400000000000000000000000000000000000
χ434-44-4-44004i−4i000000000002-2002i−2i00-22−2i2i00000000000000000000000
χ444-44-4-44004i−4i00000000000-2200−2i2i002-22i−2i00000000000000000000000
χ454-44-4-4400−4i4i000000000002-200−2i2i00-222i−2i00000000000000000000000
χ464-44-4-4400−4i4i00000000000-22002i−2i002-2−2i2i00000000000000000000000
χ474-4-44004-4000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2-22-20000000000000
χ484-4-44004-4000002i−2i2i−2i00000000000000002i−2i−2i2i−2i2i-22-220000000000000
χ494-4-44004-400000−2i2i−2i2i0000000000000000−2i2i2i−2i2i−2i-22-220000000000000
χ504-4-44004-400000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i2-22-20000000000000
χ514-4-4400-44000002i−2i2i−2i0000000000000000−2i2i2i−2i−2i2i2-2-220000000000000
χ524-4-4400-44000002i−2i2i−2i0000000000000000−2i2i−2i2i2i−2i-222-20000000000000
χ534-4-4400-4400000−2i2i−2i2i00000000000000002i−2i2i−2i−2i2i-222-20000000000000
χ544-4-4400-4400000−2i2i−2i2i00000000000000002i−2i−2i2i2i−2i2-2-220000000000000
χ5588-8-80000000004-4-44000000000000000000000000000000000000000
χ5688-8-8000000000-444-4000000000000000000000000000000000000000

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