Finite Group Databasebeta

← Group #150756

Character table — Group #150756

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41
size111122224448888888888816161616161616161616161616323232323232
order12222244444222444444444888888888888444444
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
χ5111111111111-1-1-1-11111-1-1-11111iiii−i−i−i−i-1-1ii−i−i
χ6111111111111-1-1-1-11111-1-1-11111−i−i−i−iiiii-1-1−i−iii
χ7111111111111-1-1-1-11111-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ8111111111111-1-1-1-11111-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-1-111-111-1-111-1-111-111-1-111-1-111-1-11-11-11-1
χ10111111-1-1-111-111-1-111-1-111-111-1-1-1-111-1-1111-1-11-11
χ11111111-1-1-111-111-1-111-1-111-1-1-11111-1-111-1-1-11-11-11
χ12111111-1-1-111-111-1-111-1-111-1-1-111-1-111-1-111-111-11-1
χ13111111-1-1-111-1-1-11111-1-1-1-1111-1-1ii−i−i−i−iii-11i−i−ii
χ14111111-1-1-111-1-1-11111-1-1-1-1111-1-1−i−iiiii−i−i-11−iii−i
χ15111111-1-1-111-1-1-11111-1-1-1-11-1-111ii−i−i−i−iii1-1−iii−i
χ16111111-1-1-111-1-1-11111-1-1-1-11-1-111−i−iiiii−i−i1-1i−i−ii
χ1722222222222222-2-2-2-2-2-2-2-22000000000000000000
χ18222222222222-2-222-2-2-2-222-2000000000000000000
χ19222222-2-2-222-22222-2-222-2-2-2000000000000000000
χ20222222-2-2-222-2-2-2-2-2-2-222222000000000000000000
χ212-2-222-20002-202-22i−2i002i−2i0000000i2−i22−2i2−i22−2000000
χ222-2-222-20002-202-22i−2i002i−2i0000000−i2i2−22−i2i2−22000000
χ232-2-222-20002-202-2−2i2i00−2i2i0000000i2−i2−22i2−i2−22000000
χ242-2-222-20002-202-2−2i2i00−2i2i0000000−i2i22−2−i2i22−2000000
χ252-2-222-20002-20-222i−2i00−2i2i00000002−2i2−i2−22−i2i2000000
χ262-2-222-20002-20-222i−2i00−2i2i0000000−22−i2i22−2i2−i2000000
χ272-2-222-20002-20-22−2i2i002i−2i00000002−2−i2i2−22i2−i2000000
χ282-2-222-20002-20-22−2i2i002i−2i0000000−22i2−i22−2−i2i2000000
χ29444444444-4-4-400000000000000000000000000000
χ30444444-4-4-4-4-4400000000000000000000000000000
χ314444-4-444-4000000000000002-22-200000000000000
χ324444-4-444-400000000000000-22-2200000000000000
χ334444-4-4-4-44000000000000002-2-2200000000000000
χ344444-4-4-4-4400000000000000-222-200000000000000
χ354-4-444-4000-440000000004i−4i0000000000000000000
χ364-4-444-4000-44000000000−4i4i0000000000000000000
χ3788-8-80000000000004-400000000000000000000000
χ3888-8-8000000000000-4400000000000000000000000
χ398-88-8008i−8i000000000000000000000000000000000
χ408-88-800−8i8i000000000000000000000000000000000
χ418-8-88-8800000000000000000000000000000000000

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