Finite Group Databasebeta

← Group #136255

Character table — Group #136255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111122224444888888881616161616161616161616161616161616161616161616161616
order12222222222244444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1
χ911-11-1-11-11-11-11-1-111-1ii−i−i1-1i−ii−i1-1i−ii−i1-1i−i11-1-111-1-1ii−i−i
χ1011-11-1-11-11-11-11-1-111-1ii−i−i1-1i−i−ii1-1i−i−ii1-1i−i-1-111-1-111−i−iii
χ1111-11-1-11-11-11-11-1-111-1ii−i−i1-1−iii−i-11i−ii−i-11−ii11-1-1-1-111−i−iii
χ1211-11-1-11-11-11-11-1-111-1ii−i−i1-1−ii−ii-11i−i−ii-11−ii-1-11111-1-1ii−i−i
χ1311-11-1-11-11-11-11-1-111-1−i−iii1-1i−ii−i-11−iii−i-11i−i-1-11111-1-1−i−iii
χ1411-11-1-11-11-11-11-1-111-1−i−iii1-1i−i−ii-11−ii−ii-11i−i11-1-1-1-111ii−i−i
χ1511-11-1-11-11-11-11-1-111-1−i−iii1-1−iii−i1-1−iii−i1-1−ii-1-111-1-111ii−i−i
χ1611-11-1-11-11-11-11-1-111-1−i−iii1-1−ii−ii1-1−ii−ii1-1−ii11-1-111-1-1−i−iii
χ172222222222222222-2-22222-2-2000000-2-2000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-200000022000000000000000000
χ19222222222222-2-2-2-22-20000-220000220000-2-200000000000000
χ20222222222222-2-2-2-22-20000-220000-2-200002200000000000000
χ21222222222222-2-2-2-2-2200002-2220000000000-2-2000000000000
χ22222222222222-2-2-2-2-2200002-2-2-2000000000022000000000000
χ2322-22-2-22-22-22-22-2-22-222i2i−2i−2i-22000000−2i2i000000000000000000
χ2422-22-2-22-22-22-22-2-22-22−2i−2i2i2i-220000002i−2i000000000000000000
χ2522-22-2-22-22-22-2-222-2220000-2-200002-20000-2200000000000000
χ2622-22-2-22-22-22-2-222-2220000-2-20000-2200002-200000000000000
χ2722-22-2-22-22-22-2-222-2-2-20000222i−2i0000000000−2i2i000000000000
χ2822-22-2-22-22-22-2-222-2-2-2000022−2i2i00000000002i−2i000000000000
χ292-22-22-22-2-2-22222-2-2002-22-200000000000000000000i2−i2i2−i2i2−i2i2−i2
χ302-22-22-22-2-2-22222-2-2002-22-200000000000000000000−i2i2−i2i2−i2i2−i2i2
χ312-22-22-22-2-2-22222-2-200-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i2
χ322-22-22-22-2-2-22222-2-200-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i2
χ332-2-2-2-2222-222-22-22-2002i−2i−2i2i00000000000000000000i2−i2−i2i2−222−2
χ342-2-2-2-2222-222-22-22-2002i−2i−2i2i00000000000000000000−i2i2i2−i22−2−22
χ352-2-2-2-2222-222-22-22-200−2i2i2i−2i00000000000000000000i2−i2−i2i22−2−22
χ362-2-2-2-2222-222-22-22-200−2i2i2i−2i00000000000000000000−i2i2i2−i2−222−2
χ3744444444-4-4-4-400000000000000220000-2-20000000000000000
χ3844444444-4-4-4-400000000000000-2-20000220000000000000000
χ3944-44-4-44-4-44-44000000000000002i−2i0000−2i2i0000000000000000
χ4044-44-4-44-4-44-4400000000000000−2i2i00002i−2i0000000000000000
χ414-44-44-44-444-4-4000000000000000000000000002-22-200000000
χ424-44-44-44-444-4-400000000000000000000000000-22-2200000000
χ434-44-44-44-4-4-444-4-4440000000000000000000000000000000000
χ444-4-4-4-44444-4-44000000000000000000000000002-2-2200000000
χ454-4-4-4-44444-4-4400000000000000000000000000-222-200000000
χ464-4-4-4-4444-444-4-44-440000000000000000000000000000000000
χ47888-8-8-8-88000000000000000000000000000000000000000000
χ4888-8-888-8-8000000000000000000000000000000000000000000
χ498-888-88-8-8000000000000000000000000000000000000000000
χ508-8-888-8-88000000000000000000000000000000000000000000

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