Finite Group Databasebeta

← Group #136181

Character table — Group #136181

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111122224444888888881616161616161616161616161616161616161616161616161616
order12224444224422444444888824448888888888888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-1111-11-1ii−i−i1-11-1i−ii−iii−i−ii−i11-1-1ii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-1111-11-1ii−i−i1-11-1i−ii−i−i−iiii−i-1-111−i−iii-1-111
χ111111-1-1-1-111-1-1-1-1111-11-1ii−i−i-11-11i−i−iiii−i−i−ii11-1-1−i−iii-1-111
χ121111-1-1-1-111-1-1-1-1111-11-1ii−i−i-11-11i−i−ii−i−iii−ii-1-111ii−i−i11-1-1
χ131111-1-1-1-111-1-1-1-1111-11-1−i−iii1-11-1−ii−iiii−i−i−ii-1-111ii−i−i-1-111
χ141111-1-1-1-111-1-1-1-1111-11-1−i−iii1-11-1−ii−ii−i−iii−ii11-1-1−i−iii11-1-1
χ151111-1-1-1-111-1-1-1-1111-11-1−i−iii-11-11−iii−iii−i−ii−i-1-111−i−iii11-1-1
χ161111-1-1-1-111-1-1-1-1111-11-1−i−iii-11-11−iii−i−i−iiii−i11-1-1ii−i−i-1-111
χ172222222222222222-2-2-2-222220000-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-200002200000000000000000000
χ19222222222222-2-2-2-22-2-22000022-2-20000000000000000000000
χ20222222222222-2-2-2-22-2-220000-2-2220000000000000000000000
χ21222222222222-2-2-2-2-222-20000000000220000-2-2000000000000
χ22222222222222-2-2-2-2-222-20000000000-2-2000022000000000000
χ232222-2-2-2-222-2-222-2-222-2-200002-2-220000000000000000000000
χ242222-2-2-2-222-2-222-2-222-2-20000-222-20000000000000000000000
χ252222-2-2-2-222-2-222-2-2-2-22200000000002i−2i0000−2i2i000000000000
χ262222-2-2-2-222-2-222-2-2-2-2220000000000−2i2i00002i−2i000000000000
χ272222-2-2-2-222-2-2-2-222-22-222i2i−2i−2i0000−2i2i00000000000000000000
χ282222-2-2-2-222-2-2-2-222-22-22−2i−2i2i2i00002i−2i00000000000000000000
χ292-2-2222-2-2-222-22-2-2200002i−2i2i−2i000000000000000000i2−i2i2−i22−22−2
χ302-2-2222-2-2-222-22-2-2200002i−2i2i−2i000000000000000000−i2i2−i2i2−22−22
χ312-2-2222-2-2-222-22-2-220000−2i2i−2i2i000000000000000000i2−i2i2−i2−22−22
χ322-2-2222-2-2-222-22-2-220000−2i2i−2i2i000000000000000000−i2i2−i2i22−22−2
χ332-2-22-2-222-22-22-22-2200002-2-220000000000000000002−2−222−2−22
χ342-2-22-2-222-22-22-22-2200002-2-22000000000000000000−222−2−222−2
χ352-2-22-2-222-22-22-22-220000-222-20000000000000000002−2−22−222−2
χ362-2-22-2-222-22-22-22-220000-222-2000000000000000000−222−22−2−22
χ3744444444-4-4-4-4000000000000000000002-22-200000000000000
χ3844444444-4-4-4-400000000000000000000-22-2200000000000000
χ394444-4-4-4-4-4-444000000000000000000002i−2i−2i2i00000000000000
χ404444-4-4-4-4-4-44400000000000000000000−2i2i2i−2i00000000000000
χ414-4-4444-4-44-4-44000000000000000000000000002i−2i2i−2i00000000
χ424-4-4444-4-44-4-4400000000000000000000000000−2i2i−2i2i00000000
χ434-4-4444-4-4-444-4-444-40000000000000000000000000000000000
χ444-4-44-4-4444-44-4000000000000000000000000002i−2i−2i2i00000000
χ454-4-44-4-4444-44-400000000000000000000000000−2i2i2i−2i00000000
χ464-4-44-4-444-44-444-44-40000000000000000000000000000000000
χ4788-8-88i−8i8i−8i000000000000000000000000000000000000000000
χ4888-8-8−8i8i−8i8i000000000000000000000000000000000000000000
χ498-88-88i−8i−8i8i000000000000000000000000000000000000000000
χ508-88-8−8i8i8i−8i000000000000000000000000000000000000000000

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