Finite Group Databasebeta

← Group #149820

Character table — Group #149820

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111224444444444888888888888881616161616163232323232323232
order1244242444444444248888888888888888881616161616161616
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i
χ911111111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-11-11-11-11-1
χ1011111111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-11-11-11-11
χ1111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ1211111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ1311111111111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1111-1-111-1-11
χ1411111111111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-111-1-111-1
χ1511111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1i−i−ii−iii−i
χ1611111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1−iii−ii−i−ii
χ172222222-2-2-2-222222-2-20000000022-2-2002-20000000000
χ182222222-2-2-2-222222-2-200000000-2-22200-220000000000
χ192222222-2-2-2-2-2-2-2-22220000000022-2-200-220000000000
χ202222222-2-2-2-2-2-2-2-222200000000-2-222002-20000000000
χ2122-2-22-2-222-2-20000200000022-2-22i−2i2i−2i00002i−2i00000000
χ2222-2-22-2-222-2-20000200000022-2-2−2i2i−2i2i0000−2i2i00000000
χ2322-2-22-2-222-2-200002000000-2-2222i−2i2i−2i0000−2i2i00000000
χ2422-2-22-2-222-2-200002000000-2-222−2i2i−2i2i00002i−2i00000000
χ2522-2-22-2-2-2-222000020022-2-200002i−2i−2i2i2i−2i000000000000
χ2622-2-22-2-2-2-222000020022-2-20000−2i2i2i−2i−2i2i000000000000
χ2722-2-22-2-2-2-2220000200-2-22200002i−2i−2i2i−2i2i000000000000
χ2822-2-22-2-2-2-2220000200-2-2220000−2i2i2i−2i2i−2i000000000000
χ29444444-4000044-4-4-40000000000000000000000000000
χ30444444-40000-4-444-40000000000000000000000000000
χ314444-4-400000004i−4i0002-22-22i−2i2i−2i000000000000000000
χ324444-4-400000004i−4i000-22-22−2i2i−2i2i000000000000000000
χ334444-4-40000000−4i4i0002-22-2−2i2i−2i2i000000000000000000
χ344444-4-40000000−4i4i000-22-222i−2i2i−2i000000000000000000
χ3544-4-44-4400000000-44-400000000000000000000000000
χ3644-4-44-4400000000-4-4400000000000000000000000000
χ3744-4-4-44000004i−4i000002-2-222i−2i−2i2i000000000000000000
χ3844-4-4-44000004i−4i00000-222-2−2i2i2i−2i000000000000000000
χ3944-4-4-4400000−4i4i000002-2-22−2i2i2i−2i000000000000000000
χ4044-4-4-4400000−4i4i00000-222-22i−2i−2i2i000000000000000000
χ418-88i−8i0004i−4i4-4000000000000000000000000000000000
χ428-88i−8i000−4i4i-44000000000000000000000000000000000
χ438-8−8i8i0004i−4i-44000000000000000000000000000000000
χ448-8−8i8i000−4i4i4-4000000000000000000000000000000000

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