Finite Group Databasebeta

← Group #500772

Character table — Group #500772

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122224444444444444888888888888888888888816161616161616161632323232
order12222244222244444444422222244444444444444444444488884444
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-111-1-1-1-1111111-1-11111111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-11111-1-111111111-1-111-1-111-1-1-111-1-1-1-1-1-111-1-1
χ6111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-111
χ7111111111111111-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-111
χ8111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1
χ9111111-1-11111-1-1-111111111-1-111-1-1-1-1-1-111-1-11111-1-1-11-11-111-1-11-11-1
χ10111111-1-11111-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-1-11-11-1-1-111-11-11
χ11111111-1-11111-1-1-1111111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-11-1111-1-1-11-11
χ12111111-1-11111-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1111-11-1
χ13111111-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-11
χ14111111-1-11111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-111-1
χ15111111-1-11111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-111-1-1-111-111-1
χ16111111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1111-111-111-1-11-1-11
χ17222222222-22-22-2-20000-2-20022002-200000000220000000-2-200000000
χ18222222222-22-22-2-20000-2-200-2-2002-200000000-2-200000002200000000
χ1922222222-22-222-2-20000-2-2220000-22000000220000000-2-20000000000
χ2022222222-22-222-2-20000-2-2-2-20000-22000000-2-20000000220000000000
χ2122222222-2-2-2-2222222222000000-2-20000-2-200000022-2000000000000
χ2222222222-2-2-2-2222-2-2-2-222000000-2-2000022000000-2-22000000000000
χ23222222-2-22-22-2-2220000-2-2002200-2200000000-2-200000002-200000000
χ24222222-2-22-22-2-2220000-2-200-2-200-2200000000220000000-2200000000
χ25222222-2-2-22-22-2220000-2-22200002-2000000-2-20000000-220000000000
χ26222222-2-2-22-22-2220000-2-2-2-200002-20000002200000002-20000000000
χ27222222-2-2-2-2-2-2-2-2-2222222000000220000-2-2000000-2-22000000000000
χ28222222-2-2-2-2-2-2-2-2-2-2-2-2-2220000002200002200000022-2000000000000
χ292-2-22-220022-2-200022-2-22-2000000002i2i−2i−2i2-20000000000000002i−2i0000
χ302-2-22-220022-2-200022-2-22-200000000−2i−2i2i2i2-2000000000000000−2i2i0000
χ312-2-22-220022-2-2000-2-2222-2000000002i2i−2i−2i-22000000000000000−2i2i0000
χ322-2-22-220022-2-2000-2-2222-200000000−2i−2i2i2i-220000000000000002i−2i0000
χ332-2-22-2200-2-22200022-2-22-200002-2000000-2200002-200000002-2000000
χ342-2-22-2200-2-22200022-2-22-20000-22000000-220000-220000000-22000000
χ352-2-22-2200-2-222000-2-2222-200002-20000002-200002-20000000-22000000
χ362-2-22-2200-2-222000-2-2222-20000-220000002-20000-2200000002-2000000
χ374444-4-4440000-400000000000022002-22-2000000-2-2000000000000000
χ384444-4-4440000-4000000000000-2-200-22-2200000022000000000000000
χ394444-4-4-4-4000040000000000002200-22-22000000-2-2000000000000000
χ404444-4-4-4-400004000000000000-2-2002-22-200000022000000000000000
χ4144-4-4004i−4i00000002i−2i2i−2i002-22-200000000002i−2i2i−2i002-20000000000000
χ4244-4-4004i−4i00000002i−2i2i−2i00-22-220000000000−2i2i−2i2i002-20000000000000
χ4344-4-4004i−4i0000000−2i2i−2i2i002-2-2200000000002i−2i−2i2i00-220000000000000
χ4444-4-4004i−4i0000000−2i2i−2i2i00-222-20000000000−2i2i2i−2i00-220000000000000
χ4544-4-400−4i4i00000002i−2i2i−2i002-2-220000000000−2i2i2i−2i00-220000000000000
χ4644-4-400−4i4i00000002i−2i2i−2i00-222-200000000002i−2i−2i2i00-220000000000000
χ4744-4-400−4i4i0000000−2i2i−2i2i002-22-20000000000−2i2i−2i2i002-20000000000000
χ4844-4-400−4i4i0000000−2i2i−2i2i00-22-2200000000002i−2i2i−2i002-20000000000000
χ494-4-444-400000004i−4i00000000002-2002i−2i−2i2i000000-22000000000000000
χ504-4-444-400000004i−4i0000000000-2200−2i2i2i−2i0000002-2000000000000000
χ514-4-444-40000000−4i4i00000000002-200−2i2i2i−2i000000-22000000000000000
χ524-4-444-40000000−4i4i0000000000-22002i−2i−2i2i0000002-2000000000000000
χ534-4-44-44004-4-440000000-4400000000000000000000000000000000000
χ544-4-44-4400-444-40000000-4400000000000000000000000000000000000
χ558-88-8000000000004i−4i−4i4i0000000000000000000000000000000000000
χ568-88-800000000000−4i4i4i−4i0000000000000000000000000000000000000

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