Finite Group Databasebeta

← Group #149883

Character table — Group #149883

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size111122448888888888888816161616161616163232323232323232
order1244242444888888888888444444881616161616161616
χ111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i
χ4111111111111111111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii
χ511111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111
χ711111111111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii
χ811111111111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i
χ91111111111-1-1-1-111111111-1-1-1-1-1-1111-11-11-11-1
χ101111111111-1-1-1-111111111-1-1-1-1-1-111-11-11-11-11
χ111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−i−ii−ii
χ121111111111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−iii−ii−i
χ131111111111-1-1-1-1-1-1-1-11111-1-11111-1-11-1-111-1-11
χ141111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1-111-1
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111i−i−ii−iii−i
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−iii−ii−i−ii
χ1722222222-2-222-2-2000022-2-22-200000000000000
χ1822222222-2-222-2-20000-2-222-2200000000000000
χ1922222222-2-2-2-222000022-2-2-2200000000000000
χ2022222222-2-2-2-2220000-2-2222-200000000000000
χ2122-2-22-2-222-2000000002i−2i2i−2i002-22i−2i0000000000
χ2222-2-22-2-222-2000000002i−2i2i−2i00-22−2i2i0000000000
χ2322-2-22-2-222-200000000−2i2i−2i2i002-2−2i2i0000000000
χ2422-2-22-2-222-200000000−2i2i−2i2i00-222i−2i0000000000
χ2522-2-22-2-22-22000022-2-22i−2i−2i2i0000002i−2i00000000
χ2622-2-22-2-22-22000022-2-2−2i2i2i−2i000000−2i2i00000000
χ2722-2-22-2-22-220000-2-2222i−2i−2i2i000000−2i2i00000000
χ2822-2-22-2-22-220000-2-222−2i2i2i−2i0000002i−2i00000000
χ29444444-4-400004-4000000000000000000000000
χ30444444-4-40000-44000000000000000000000000
χ3144-4-44-44-4004i−4i00000000000000000000000000
χ3244-4-44-44-400−4i4i00000000000000000000000000
χ338888-8-800000000000000000000000000000000
χ3488-8-8-8800000000000000000000000000000000
χ358-88i−8i00000000002i2−2i222−2200000000000000000000
χ368-88i−8i0000000000−2i22i2−222200000000000000000000
χ378-8−8i8i00000000002i2−2i2−222200000000000000000000
χ388-8−8i8i0000000000−2i22i222−2200000000000000000000

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