Finite Group Databasebeta

← Group #136178

Character table — Group #136178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111122224444888888881616161616161616161616161616161616161616161616161616
order12222222222244444444444422444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ911-111-1-1-11-11-11-1-111-1ii−i−i1-11-1i−ii−ii−ii−i1-1i−i11-1-1ii−i−i11-1-1
χ1011-111-1-1-11-11-11-1-111-1ii−i−i1-11-1i−i−iii−i−ii1-1i−i-1-111−i−iii-1-111
χ1111-111-1-1-11-11-11-1-111-1ii−i−i1-1-11i−ii−i−iii−i-11−ii11-1-1−i−iii-1-111
χ1211-111-1-1-11-11-11-1-111-1ii−i−i1-1-11i−i−ii−ii−ii-11−ii-1-111ii−i−i11-1-1
χ1311-111-1-1-11-11-11-1-111-1−i−iii1-11-1−iii−i−iii−i1-1−ii-1-111ii−i−i-1-111
χ1411-111-1-1-11-11-11-1-111-1−i−iii1-11-1−ii−ii−ii−ii1-1−ii11-1-1−i−iii11-1-1
χ1511-111-1-1-11-11-11-1-111-1−i−iii1-1-11−iii−ii−ii−i-11i−i-1-111−i−iii11-1-1
χ1611-111-1-1-11-11-11-1-111-1−i−iii1-1-11−ii−iii−i−ii-11i−i11-1-1ii−i−i-1-111
χ172222222222222222-2-22222-2-200-2-20000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-200220000000000000000000000
χ19222222222222-2-2-2-22-20000-222200000000-2-200000000000000
χ20222222222222-2-2-2-22-20000-22-2-2000000002200000000000000
χ21222222222222-2-2-2-2-2200002-2000000220000-2-2000000000000
χ22222222222222-2-2-2-2-2200002-2000000-2-2000022000000000000
χ2322-222-2-2-22-22-22-2-22-222i2i−2i−2i-2200−2i2i0000000000000000000000
χ2422-222-2-2-22-22-22-2-22-22−2i−2i2i2i-22002i−2i0000000000000000000000
χ2522-222-2-2-22-22-2-222-2220000-2-22-200000000-2200000000000000
χ2622-222-2-2-22-22-2-222-2220000-2-2-22000000002-200000000000000
χ2722-222-2-2-22-22-2-222-2-2-20000220000002i−2i0000−2i2i000000000000
χ2822-222-2-2-22-22-2-222-2-2-2000022000000−2i2i00002i−2i000000000000
χ292-222-22-2-2-222-2-22-22002i−2i2i−2i00000000000000000000i2−i2i2−i22−22−2
χ302-222-22-2-2-222-2-22-22002i−2i2i−2i00000000000000000000−i2i2−i2i2−22−22
χ312-222-22-2-2-222-2-22-2200−2i2i−2i2i00000000000000000000i2−i2i2−i2−22−22
χ322-222-22-2-2-222-2-22-2200−2i2i−2i2i00000000000000000000−i2i2−i2i22−22−2
χ332-2-22-2-222-2-222-2-222002-2-22000000000000000000002−2−222−2−22
χ342-2-22-2-222-2-222-2-222002-2-2200000000000000000000−222−2−222−2
χ352-2-22-2-222-2-222-2-22200-222-2000000000000000000002−2−22−222−2
χ362-2-22-2-222-2-222-2-22200-222-200000000000000000000−222−22−2−22
χ3744444444-4-4-4-400000000000000002200-2-20000000000000000
χ3844444444-4-4-4-40000000000000000-2-200220000000000000000
χ3944-444-4-4-4-44-4400000000000000002i−2i00−2i2i0000000000000000
χ4044-444-4-4-4-44-440000000000000000−2i2i002i−2i0000000000000000
χ414-444-44-4-44-4-44000000000000000000000000002i−2i2i−2i00000000
χ424-444-44-4-44-4-4400000000000000000000000000−2i2i−2i2i00000000
χ434-444-44-4-4-444-44-44-40000000000000000000000000000000000
χ444-4-44-4-44444-4-4000000000000000000000000002i−2i−2i2i00000000
χ454-4-44-4-44444-4-400000000000000000000000000−2i2i2i−2i00000000
χ464-4-44-4-444-4-44444-4-40000000000000000000000000000000000
χ47888-8-8-88-8000000000000000000000000000000000000000000
χ4888-8-8-88-88000000000000000000000000000000000000000000
χ498-88-88-8-88000000000000000000000000000000000000000000
χ508-8-8-8888-8000000000000000000000000000000000000000000

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