Finite Group Databasebeta

← Group #136170

Character table — Group #136170

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1
χ911-1-11-11-111-1-11-1-111-1ii−i−iii−i−iii−i−i11-1-1-11i−i1-1i−ii−i11-1-111-1-1ii−i−i
χ1011-1-11-11-111-1-11-1-111-1ii−i−iii−i−iii−i−i11-1-1-11−ii1-1−iii−i-1-111-1-111−i−iii
χ1111-1-11-11-111-1-11-1-111-1ii−i−i−i−iiiii−i−i-1-111-11i−i-11i−i−ii11-1-1-1-111−i−iii
χ1211-1-11-11-111-1-11-1-111-1ii−i−i−i−iiiii−i−i-1-111-11−ii-11−ii−ii-1-11111-1-1ii−i−i
χ1311-1-11-11-111-1-11-1-111-1−i−iiiii−i−i−i−iii-1-111-11i−i-11i−ii−i-1-11111-1-1−i−iii
χ1411-1-11-11-111-1-11-1-111-1−i−iiiii−i−i−i−iii-1-111-11−ii-11−iii−i11-1-1-1-111ii−i−i
χ1511-1-11-11-111-1-11-1-111-1−i−iii−i−iii−i−iii11-1-1-11i−i1-1i−i−ii-1-111-1-111ii−i−i
χ1611-1-11-11-111-1-11-1-111-1−i−iii−i−iii−i−iii11-1-1-11−ii1-1−ii−ii11-1-111-1-1−i−iii
χ172222222222222222-2-222220000-2-2-2-20000-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2000022220000-2-200000000000000000000
χ19222222222222-2-2-2-22-200000000000022222-200-2-20000000000000000
χ20222222222222-2-2-2-22-2000000000000-2-2-2-22-200220000000000000000
χ21222222222222-2-2-2-2-220000222200000000-22000000-2-2000000000000
χ22222222222222-2-2-2-2-220000-2-2-2-200000000-2200000022000000000000
χ232222-2-2-2-22-22-222-2-200000000002-22-20000000000000000002−22−22−22−2
χ242222-2-2-2-22-22-222-2-200000000002-22-2000000000000000000−22−22−22−22
χ252222-2-2-2-22-22-222-2-20000000000-22-220000000000000000002−22−2−22−22
χ262222-2-2-2-22-22-222-2-20000000000-22-22000000000000000000−22−222−22−2
χ2722-2-22-22-222-2-22-2-22-222i2i−2i−2i0000−2i−2i2i2i00002-200000000000000000000
χ2822-2-22-22-222-2-22-2-22-22−2i−2i2i2i00002i2i−2i−2i00002-200000000000000000000
χ2922-2-22-22-222-2-2-222-22200000000000022-2-2-2-200-220000000000000000
χ3022-2-22-22-222-2-2-222-222000000000000-2-222-2-2002-20000000000000000
χ3122-2-22-22-222-2-2-222-2-2-200002i2i−2i−2i0000000022000000−2i2i000000000000
χ3222-2-22-22-222-2-2-222-2-2-20000−2i−2i2i2i00000000220000002i−2i000000000000
χ3322-2-2-22-222-2-222-22-200000000002i−2i−2i2i0000000000000000002−2−22i2−i2−i2i2
χ3422-2-2-22-222-2-222-22-200000000002i−2i−2i2i000000000000000000−222−2−i2i2i2−i2
χ3522-2-2-22-222-2-222-22-20000000000−2i2i2i−2i0000000000000000002−2−22−i2i2i2−i2
χ3622-2-2-22-222-2-222-22-20000000000−2i2i2i−2i000000000000000000−222−2i2−i2−i2i2
χ3744444444-4-4-4-40000000000000000000000002200-2-200000000000000
χ3844444444-4-4-4-4000000000000000000000000-2-2002200000000000000
χ394444-4-4-4-44-44-4-4-4440000000000000000000000000000000000000000
χ404444-4-4-4-4-44-44000000000000000000000000000000002-22-200000000
χ414444-4-4-4-4-44-4400000000000000000000000000000000-22-2200000000
χ4244-4-44-44-4-4-4440000000000000000000000002i−2i00−2i2i00000000000000
χ4344-4-44-44-4-4-444000000000000000000000000−2i2i002i−2i00000000000000
χ4444-4-4-44-444-4-44-44-440000000000000000000000000000000000000000
χ4544-4-4-44-44-444-4000000000000000000000000000000002-2-2200000000
χ4644-4-4-44-44-444-400000000000000000000000000000000-222-200000000
χ474-44-4-444-400000000002i−2i2i−2i2i−2i2i−2i00002-22-20000000000000000000000
χ484-44-4-444-400000000002i−2i2i−2i−2i2i−2i2i0000-22-220000000000000000000000
χ494-44-4-444-40000000000−2i2i−2i2i2i−2i2i−2i0000-22-220000000000000000000000
χ504-44-4-444-40000000000−2i2i−2i2i−2i2i−2i2i00002-22-20000000000000000000000
χ514-4-44-4-44400000000002-2-222-2-2200002-2-220000000000000000000000
χ524-4-44-4-44400000000002-2-22-222-20000-222-20000000000000000000000
χ534-4-44-4-4440000000000-222-22-2-220000-222-20000000000000000000000
χ544-4-44-4-4440000000000-222-2-222-200002-2-220000000000000000000000
χ558-88-88-8-88000000000000000000000000000000000000000000000000
χ568-8-8888-8-8000000000000000000000000000000000000000000000000

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