Finite Group Databasebeta

← Group #150753

Character table — Group #150753

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41
size111122224448888888888816161616161616161616161616323232323232
order12222222244224444444442888888888888244444
χ111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-11-1-11111-1-1-11111iiii−i−i−i−i-1-1ii−i−i
χ611111111111-1-11-1-11111-1-1-11111−i−i−i−iiiii-1-1−i−iii
χ711111111111-1-11-1-11111-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111111-1-11-1-11111-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ911111-1-11-11111-1-1-111-1-111-111-1-111-1-111-1-11-11-11-1
χ1011111-1-11-11111-1-1-111-1-111-111-1-1-1-111-1-1111-1-11-11
χ1111111-1-11-11111-1-1-111-1-111-1-1-11111-1-111-1-1-11-11-11
χ1211111-1-11-11111-1-1-111-1-111-1-1-111-1-111-1-111-111-11-1
χ1311111-1-11-111-1-1-11111-1-1-1-1111-1-1ii−i−i−i−iii-11i−i−ii
χ1411111-1-11-111-1-1-11111-1-1-1-1111-1-1−i−iiiii−i−i-11−iii−i
χ1511111-1-11-111-1-1-11111-1-1-1-11-1-111ii−i−i−i−iii1-1−iii−i
χ1611111-1-11-111-1-1-11111-1-1-1-11-1-111−i−iiiii−i−i1-1i−i−ii
χ1722222222222222-2-2-2-2-2-2-2-22000000000000000000
χ1822222222222-2-2222-2-2-2-222-2000000000000000000
χ1922222-2-22-22222-222-2-222-2-2-2000000000000000000
χ2022222-2-22-222-2-2-2-2-2-2-222222000000000000000000
χ2122-2-2200-202-22-202i−2i002i−2i0000000i2−i22−2i2−i22−2000000
χ2222-2-2200-202-22-202i−2i002i−2i0000000−i2i2−22−i2i2−22000000
χ2322-2-2200-202-22-20−2i2i00−2i2i0000000i2−i2−22i2−i2−22000000
χ2422-2-2200-202-22-20−2i2i00−2i2i0000000−i2i22−2−i2i22−2000000
χ2522-2-2200-202-2-2202i−2i00−2i2i00000002−2i2−i2−22−i2i2000000
χ2622-2-2200-202-2-2202i−2i00−2i2i0000000−22−i2i22−2i2−i2000000
χ2722-2-2200-202-2-220−2i2i002i−2i00000002−2−i2i2−22i2−i2000000
χ2822-2-2200-202-2-220−2i2i002i−2i0000000−22i2−i22−2−i2i2000000
χ29444444444-4-400-4000000000000000000000000000
χ3044444-4-44-4-4-4004000000000000000000000000000
χ314444-444-4-4000000000000002-22-200000000000000
χ324444-444-4-400000000000000-22-2200000000000000
χ334444-4-4-4-44000000000000002-2-2200000000000000
χ344444-4-4-4-4400000000000000-222-200000000000000
χ3544-4-4400-40-440000000004i−4i0000000000000000000
χ3644-4-4400-40-44000000000−4i4i0000000000000000000
χ3788-8-8-8008000000000000000000000000000000000
χ388-88-80000000000004-400000000000000000000000
χ398-88-8000000000000-4400000000000000000000000
χ408-8-8808-80000000000000000000000000000000000
χ418-8-880-880000000000000000000000000000000000

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