Finite Group Databasebeta

← Group #500757

Character table — Group #500757

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122224444444444444888888888888888888888816161616161616161632323232
order12222244222222224444422222244444444444444442244444444488
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-11-1-1-1-1111-1-111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-11-1-1-1-1111-1-111-1-1-1-1-1-11-1-1-1-1-1-11111
χ5111111111-1-1-1-111111111111111111111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ6111111111-1-1-1-1111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ7111111111-1-1-1-111111111-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-111
χ8111111111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1111111-1-1-1111111-1-1
χ9111111-1-1111111111-1-1-1111-1-111-111-1-1-1-1-1-1-11111-1-11-1-11-111-1-11-11-1
χ10111111-1-1111111111-1-1-1111-1-1-1-1-1-1-111-1-1-1111111-1-11-1-11-1-1-111-11-11
χ11111111-1-1111111111-1-1-11-1-11111-111-1-1-1-1-1-1-111-1-111-11-1-1111-1-1-11-11
χ12111111-1-1111111111-1-1-11-1-111-1-1-1-1-111-1-1-11111-1-111-11-1-11-1-1111-11-1
χ13111111-1-11-1-1-1-11111-1-1-1111-1-111-111-1-1-111-1-1-1-1-1-111-1111-1-1-1111-1-11
χ14111111-1-11-1-1-1-11111-1-1-1111-1-1-1-1-1-1-111-11111-1-1-1-111-1111-111-1-1-111-1
χ15111111-1-11-1-1-1-11111-1-1-11-1-11111-111-1-1-111-1-1-1-111-1-11-11-11-1-111-111-1
χ16111111-1-11-1-1-1-11111-1-1-11-1-111-1-1-1-1-111-11111-1-111-1-11-11-1111-1-11-1-11
χ172222222220000-2-22-22-2-2-2222200-2000020000000000000-2-200000000
χ182222222220000-2-22-22-2-2-2-2-2-2-200-20000200000000000002200000000
χ1922222222-20000-2-2-222-2-2200000020000-20000002222-2-200000000000
χ2022222222-20000-2-2-222-2-2200000020000-2000000-2-2-2-22200000000000
χ2122222222-2222222-2-2222-2000000-20000-22200-2-2000000-20000000000
χ2222222222-2-2-2-2-222-2-2222-2000000-20000-2-2-2002200000020000000000
χ23222222-2-220000-2-22-2-222-222-2-20020000-20000000000000-2200000000
χ24222222-2-220000-2-22-2-222-2-2-2220020000-200000000000002-200000000
χ25222222-2-2-20000-2-2-22-2222000000-20000200000022-2-2-2200000000000
χ26222222-2-2-20000-2-2-22-2222000000-200002000000-2-2222-200000000000
χ27222222-2-2-2222222-2-2-2-2-2-2000000200002-2-200-2-200000020000000000
χ28222222-2-2-2-2-2-2-222-2-2-2-2-2-2000000200002220022000000-20000000000
χ2922-2-2-2200222-2-22-2-22000-20000000002i−2i0002i−2i2-2000000000002i−2i0000
χ3022-2-2-2200222-2-22-2-22000-2000000000−2i2i000−2i2i2-200000000000−2i2i0000
χ3122-2-2-22002-2-2222-2-22000-20000000002i−2i0002i−2i-2200000000000−2i2i0000
χ3222-2-2-22002-2-2222-2-22000-2000000000−2i2i000−2i2i-22000000000002i−2i0000
χ3322-2-2-2200-222-2-22-22-2000200002-202-20000000-220000000002-2000000
χ3422-2-2-2200-222-2-22-22-200020000-220-220000000-22000000000-22000000
χ3522-2-2-2200-2-2-2222-22-2000200002-202-200000002-2000000000-22000000
χ3622-2-2-2200-2-2-2222-22-200020000-220-2200000002-20000000002-2000000
χ374444-4-444000000000-40000000220-2-2-2-2000220000000000000000000
χ384444-4-444000000000-40000000-2-202222000-2-20000000000000000000
χ394444-4-4-4-400000000040000000220-2-222000-2-20000000000000000000
χ404444-4-4-4-400000000040000000-2-2022-2-2000220000000000000000000
χ4144-4-44-40000000000004i−4i000002-20-222i−2i000−2i2i0000000000000000000
χ4244-4-44-40000000000004i−4i00000-2202-2−2i2i0002i−2i0000000000000000000
χ4344-4-44-4000000000000−4i4i000002-20-22−2i2i0002i−2i0000000000000000000
χ4444-4-44-4000000000000−4i4i00000-2202-22i−2i000−2i2i0000000000000000000
χ4544-4-4-440040000-44-4-4000400000000000000000000000000000000000
χ4644-4-4-4400-40000-4444000-400000000000000000000000000000000000
χ474-4-44004-402-22-2000000002-22-2000000002-200002-22-20000000000000
χ484-4-44004-402-22-200000000-22-22000000002-20000-22-220000000000000
χ494-4-44004-40-22-22000000002-22-200000000-220000-22-220000000000000
χ504-4-44004-40-22-2200000000-22-2200000000-2200002-22-20000000000000
χ514-4-4400-4402-22-2000000002-2-2200000000-2200002-2-220000000000000
χ524-4-4400-4402-22-200000000-222-200000000-220000-222-20000000000000
χ534-4-4400-440-22-22000000002-2-22000000002-20000-222-20000000000000
χ544-4-4400-440-22-2200000000-222-2000000002-200002-2-220000000000000
χ558-88-8000004-4-440000000000000000000000000000000000000000000
χ568-88-800000-444-40000000000000000000000000000000000000000000

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