Finite Group Databasebeta

← Group #136193

Character table — Group #136193

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222224444888888888888161616161616161616161616161616161616161616161616
order1244222444224444448888888824444444888888881616161616161616
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ711111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ811111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911-1-1-11-111-1-111-1ii−i−i1-1ii−i−i1-11-11-111-1-1i−iii−i−ii−i11-1-1ii−i−i
χ1011-1-1-11-111-1-111-1ii−i−i1-1ii−i−i1-11-11-1-1-111i−i−i−iiii−i-1-111−i−iii
χ1111-1-1-11-111-1-111-1ii−i−i1-1ii−i−i1-1-11-1111-1-1−iiii−i−i−ii-1-111−i−iii
χ1211-1-1-11-111-1-111-1ii−i−i1-1ii−i−i1-1-11-11-1-111−ii−i−iii−ii11-1-1ii−i−i
χ1311-1-1-11-111-1-111-1−i−iii1-1−i−iii1-11-11-111-1-1−ii−i−iii−ii11-1-1−i−iii
χ1411-1-1-11-111-1-111-1−i−iii1-1−i−iii1-11-11-1-1-111−iiii−i−i−ii-1-111ii−i−i
χ1511-1-1-11-111-1-111-1−i−iii1-1−i−iii1-1-11-1111-1-1i−i−i−iiii−i-1-111ii−i−i
χ1611-1-1-11-111-1-111-1−i−iii1-1−i−iii1-1-11-11-1-111i−iii−i−ii−i11-1-1−i−iii
χ17222222222222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-22222-2-2000000000000000000000000
χ192222222222-2-2-2-200002-20000-2222-2-200000000000000000000
χ202222222222-2-2-2-200002-20000-22-2-22200000000000000000000
χ212222222222-2-2-2-20000-2200002-200000000220000-2-200000000
χ222222222222-2-2-2-20000-2200002-200000000-2-200002200000000
χ232222-22-2-2-22-22-220000002-22-20000000000000000002−22−22−22−2
χ242222-22-2-2-22-22-220000002-22-2000000000000000000−22−22−22−22
χ252222-22-2-2-22-22-22000000-22-220000000000000000002−22−2−22−22
χ262222-22-2-2-22-22-22000000-22-22000000000000000000−22−222−22−2
χ2722-2-2222-2-2-222-2-20000002i−2i−2i2i0000000000000000002−2−22i2−i2−i2i2
χ2822-2-2222-2-2-222-2-20000002i−2i−2i2i000000000000000000−222−2−i2i2i2−i2
χ2922-2-2222-2-2-222-2-2000000−2i2i2i−2i0000000000000000002−2−22−i2i2i2−i2
χ3022-2-2222-2-2-222-2-2000000−2i2i2i−2i000000000000000000−222−2i2−i2−i2i2
χ3122-2-2-22-222-22-2-220000220000-2-22-2-2200000000000000000000
χ3222-2-2-22-222-22-2-220000220000-2-2-222-200000000000000000000
χ3322-2-2-22-222-22-2-220000-2-2000022000000002i−2i0000−2i2i00000000
χ3422-2-2-22-222-22-2-220000-2-200002200000000−2i2i00002i−2i00000000
χ3522-2-2-22-222-2-222-22i2i−2i−2i-22−2i−2i2i2i-22000000000000000000000000
χ3622-2-2-22-222-2-222-2−2i−2i2i2i-222i2i−2i−2i-22000000000000000000000000
χ3744444-4-44-4-4000000000000000000002i−2i2i−2i0000000000000000
χ3844444-4-44-4-400000000000000000000−2i2i−2i2i0000000000000000
χ394444-44-4-4-444-44-4000000000000000000000000000000000000
χ404444-4-44-44-4000000000000000000000000002-22-20000000000
χ414444-4-44-44-400000000000000000000000000-22-220000000000
χ4244-4-4444-4-4-4-4-444000000000000000000000000000000000000
χ4344-4-44-4-4-444000000000000000000000000002i−2i−2i2i0000000000
χ4444-4-44-4-4-44400000000000000000000000000−2i2i2i−2i0000000000
χ4544-4-4-4-444-44000000000000000000002i−2i−2i2i0000000000000000
χ4644-4-4-4-444-4400000000000000000000−2i2i2i−2i0000000000000000
χ478-88i−8i00000000002+2i−2−2i2−2i−2+2i00000000000000000000000000000000
χ488-88i−8i0000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000000000
χ498-8−8i8i00000000002−2i−2+2i2+2i−2−2i00000000000000000000000000000000
χ508-8−8i8i0000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000000000

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