Finite Group Databasebeta

← Group #136248

Character table — Group #136248

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1
χ611111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111
χ711111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ9111-1-1-1-1111-1-11-1-111ii−i−i-111-1-1ii−i−iii−i−i-11i−iii−i−i1-111-1-1ii−i−i11-1-1
χ10111-1-1-1-1111-1-11-1-111ii−i−i-111-1-1ii−i−iii−i−i-11i−i−i−iii1-1-1-111−i−iii-1-111
χ11111-1-1-1-1111-1-11-1-111ii−i−i-1-1-111ii−i−i−i−iii-11−iiii−i−i-1111-1-1−i−iii-1-111
χ12111-1-1-1-1111-1-11-1-111ii−i−i-1-1-111ii−i−i−i−iii-11−ii−i−iii-11-1-111ii−i−i11-1-1
χ13111-1-1-1-1111-1-11-1-111−i−iii-111-1-1−i−iii−i−iii-11−iiii−i−i1-1-1-111ii−i−i-1-111
χ14111-1-1-1-1111-1-11-1-111−i−iii-111-1-1−i−iii−i−iii-11−ii−i−iii1-111-1-1−i−iii11-1-1
χ15111-1-1-1-1111-1-11-1-111−i−iii-1-1-111−i−iiiii−i−i-11i−iii−i−i-11-1-111−i−iii11-1-1
χ16111-1-1-1-1111-1-11-1-111−i−iii-1-1-111−i−iiiii−i−i-11i−i−i−iii-1111-1-1ii−i−i-1-111
χ172222222222222222-22222-20000-2-2-2-20000-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2000022220000-2-200000000000000000000
χ19222222222222-2-2-2-220000-22222000000002-2000000-2-2000000000000
χ20222222222222-2-2-2-220000-2-2-2-2-2000000002-200000022000000000000
χ21222222222222-2-2-2-2-200002000000002222-22-2-2000000000000000000
χ22222222222222-2-2-2-2-20000200000000-2-2-2-2-2222000000000000000000
χ23222-2-2-2-2222-2-22-2-22-22i2i−2i−2i20000−2i−2i2i2i00002-200000000000000000000
χ24222-2-2-2-2222-2-22-2-22-2−2i−2i2i2i200002i2i−2i−2i00002-200000000000000000000
χ25222-2-2-2-2222-2-2-222-220000222-2-200000000-2-2000000-22000000000000
χ26222-2-2-2-2222-2-2-222-2200002-2-22200000000-2-20000002-2000000000000
χ27222-2-2-2-2222-2-2-222-2-20000-2000000002i2i−2i−2i22−2i2i000000000000000000
χ28222-2-2-2-2222-2-2-222-2-20000-200000000−2i−2i2i2i222i−2i000000000000000000
χ2922-222-2-2-22-22-2-22-2200000000002i−2i2i−2i0000000000000000002−22−2i2−i2i2−i2
χ3022-222-2-2-22-22-2-22-2200000000002i−2i2i−2i000000000000000000−22−22−i2i2−i2i2
χ3122-222-2-2-22-22-2-22-220000000000−2i2i−2i2i0000000000000000002−22−2−i2i2−i2i2
χ3222-222-2-2-22-22-2-22-220000000000−2i2i−2i2i000000000000000000−22−22i2−i2i2−i2
χ3322-2-2-222-22-2-22-2-22200000000002-2-22000000000000000000i2−i2−i2i2−i2i2i2−i2
χ3422-2-2-222-22-2-22-2-22200000000002-2-22000000000000000000−i2i2i2−i2i2−i2−i2i2
χ3522-2-2-222-22-2-22-2-2220000000000-222-2000000000000000000i2−i2−i2i2i2−i2−i2i2
χ3622-2-2-222-22-2-22-2-2220000000000-222-2000000000000000000−i2i2i2−i2−i2i2i2−i2
χ3744444444-4-4-4-4000000000000000000000000002-22-200000000000000
χ3844444444-4-4-4-400000000000000000000000000-22-2200000000000000
χ39444-4-4-4-44-4-444000000000000000000000000002i−2i−2i2i00000000000000
χ40444-4-4-4-44-4-44400000000000000000000000000−2i2i2i−2i00000000000000
χ4144-444-4-4-44-44-44-44-40000000000000000000000000000000000000000
χ4244-444-4-4-4-44-44000000000000000000000000000000002i−2i2i−2i00000000
χ4344-444-4-4-4-44-4400000000000000000000000000000000−2i2i−2i2i00000000
χ4444-4-4-444-44-4-4444-4-40000000000000000000000000000000000000000
χ4544-4-4-444-4-444-4000000000000000000000000000000002i−2i−2i2i00000000
χ4644-4-4-444-4-444-400000000000000000000000000000000−2i2i2i−2i00000000
χ474-444-44-4-40000000002-22-202i−2i2i−2i00002i−2i2i−2i0000000000000000000000
χ484-444-44-4-40000000002-22-20−2i2i−2i2i0000−2i2i−2i2i0000000000000000000000
χ494-444-44-4-4000000000-22-2202i−2i2i−2i0000−2i2i−2i2i0000000000000000000000
χ504-444-44-4-4000000000-22-220−2i2i−2i2i00002i−2i2i−2i0000000000000000000000
χ514-44-44-44-40000000002i−2i−2i2i02i−2i−2i2i0000-222-20000000000000000000000
χ524-44-44-44-40000000002i−2i−2i2i0−2i2i2i−2i00002-2-220000000000000000000000
χ534-44-44-44-4000000000−2i2i2i−2i02i−2i−2i2i00002-2-220000000000000000000000
χ544-44-44-44-4000000000−2i2i2i−2i0−2i2i2i−2i0000-222-20000000000000000000000
χ558-8-88-8-888000000000000000000000000000000000000000000000000
χ568-8-8-888-88000000000000000000000000000000000000000000000000

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