Finite Group Databasebeta

← Group #137336

Character table — Group #137336

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111122224444888888881616161616161616161616161616161616161616161616161616
order12224444224422444444888844444444888888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ91111-1-1-1-111-1-111-1-11-11-1ii−i−i11-1-11-11-1i−ii−ii−iii−i−i11-1-1ii−i−i
χ101111-1-1-1-111-1-111-1-11-11-1ii−i−i11-1-1-11-11−iii−i−iiii−i−i-1-111−i−iii
χ111111-1-1-1-111-1-111-1-11-11-1ii−i−i-1-1111-11-1i−ii−ii−i−i−iii-1-111−i−iii
χ121111-1-1-1-111-1-111-1-11-11-1ii−i−i-1-111-11-11−iii−i−ii−i−iii11-1-1ii−i−i
χ131111-1-1-1-111-1-111-1-11-11-1−i−iii11-1-11-11-1−ii−ii−ii−i−iii11-1-1−i−iii
χ141111-1-1-1-111-1-111-1-11-11-1−i−iii11-1-1-11-11i−i−iii−i−i−iii-1-111ii−i−i
χ151111-1-1-1-111-1-111-1-11-11-1−i−iii-1-1111-11-1−ii−ii−iiii−i−i-1-111ii−i−i
χ161111-1-1-1-111-1-111-1-11-11-1−i−iii-1-111-11-11i−i−iii−iii−i−i11-1-1−i−iii
χ172222222222222222-2-2-2-222220000000000-2-200000000000000
χ182222222222222222-2-2-2-2-2-2-2-200000000002200000000000000
χ19222222222222-2-2-2-22-2-220000000000002200-2-2000000000000
χ20222222222222-2-2-2-22-2-22000000000000-2-20022000000000000
χ21222222222222-2-2-2-2-222-20000000022-2-2000000000000000000
χ22222222222222-2-2-2-2-222-200000000-2-222000000000000000000
χ232222-2-2-2-222-2-222-2-2-22-222i2i−2i−2i0000000000−2i2i00000000000000
χ242222-2-2-2-222-2-222-2-2-22-22−2i−2i2i2i00000000002i−2i00000000000000
χ252222-2-2-2-222-2-2-2-22222-2-20000000000002i−2i00−2i2i000000000000
χ262222-2-2-2-222-2-2-2-22222-2-2000000000000−2i2i002i−2i000000000000
χ272222-2-2-2-222-2-2-2-222-2-222000000002-2-22000000000000000000
χ282222-2-2-2-222-2-2-2-222-2-22200000000-222-2000000000000000000
χ2922-2-222-2-22-22-22-22-200002-22-20000000000000000002−22−22−22−2
χ3022-2-222-2-22-22-22-22-200002-22-2000000000000000000−22−22−22−22
χ3122-2-222-2-22-22-22-22-20000-22-220000000000000000002−22−2−22−22
χ3222-2-222-2-22-22-22-22-20000-22-22000000000000000000−22−222−22−2
χ3322-2-2-2-2222-2-222-2-2200002i−2i−2i2i0000000000000000002−2−22i2−i2−i2i2
χ3422-2-2-2-2222-2-222-2-2200002i−2i−2i2i000000000000000000−222−2−i2i2i2−i2
χ3522-2-2-2-2222-2-222-2-220000−2i2i2i−2i0000000000000000002−2−22−i2i2i2−i2
χ3622-2-2-2-2222-2-222-2-220000−2i2i2i−2i000000000000000000−222−2i2−i2−i2i2
χ3744444444-4-4-4-40000000000002-22-20000000000000000000000
χ3844444444-4-4-4-4000000000000-22-220000000000000000000000
χ394444-4-4-4-4-4-4440000000000002-2-220000000000000000000000
χ404444-4-4-4-4-4-444000000000000-222-20000000000000000000000
χ4144-4-444-4-44-44-4-44-440000000000000000000000000000000000
χ4244-4-444-4-4-44-44000000000000000000000000002i−2i2i−2i00000000
χ4344-4-444-4-4-44-4400000000000000000000000000−2i2i−2i2i00000000
χ4444-4-4-4-4444-4-44-444-40000000000000000000000000000000000
χ4544-4-4-4-444-444-4000000000000000000000000002-2-2200000000
χ4644-4-4-4-444-444-400000000000000000000000000-222-200000000
χ478-88-88i−8i8i−8i000000000000000000000000000000000000000000
χ488-88-8−8i8i−8i8i000000000000000000000000000000000000000000
χ498-8-888i−8i−8i8i000000000000000000000000000000000000000000
χ508-8-88−8i8i8i−8i000000000000000000000000000000000000000000

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