Finite Group Databasebeta

← Group #149792

Character table — Group #149792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222222444488888888888888881616161616163232323232323232
order1244244444244424444444444488882444881616161616161616
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
χ5111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i
χ911111-1-1-1-1111-1-1-1-1111111-1-1-1-1111111-1-1-1-11-11-11-11-1
χ1011111-1-1-1-1111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-11-11-11-11
χ1111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ1211111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ1311111-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-111-1-11-1-111-1-11
χ1411111-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-111-1-1-111-1-111-1
χ1511111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111i−i−ii−iii−i
χ1611111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111−iii−ii−i−ii
χ1722222222222222-2-2-2-20000000022-2-200002-200000000
χ1822222222222222-2-2-2-200000000-2-2220000-2200000000
χ1922222-2-2-2-2222-2-222-2-20000000022-2-20000-2200000000
χ2022222-2-2-2-2222-2-222-2-200000000-2-22200002-200000000
χ2122-2-220000-2-2200002-200002i2i−2i−2i2i−2i2i−2i002-20000000000
χ2222-2-220000-2-2200002-200002i2i−2i−2i−2i2i−2i2i00-220000000000
χ2322-2-220000-2-2200002-20000−2i−2i2i2i2i−2i2i−2i00-220000000000
χ2422-2-220000-2-2200002-20000−2i−2i2i2i−2i2i−2i2i002-20000000000
χ2522-2-220000-2-220000-222i2i−2i−2i00002i−2i−2i2i2-2000000000000
χ2622-2-220000-2-220000-222i2i−2i−2i0000−2i2i2i−2i-22000000000000
χ2722-2-220000-2-220000-22−2i−2i2i2i00002i−2i−2i2i-22000000000000
χ2822-2-220000-2-220000-22−2i−2i2i2i0000−2i2i2i−2i2-2000000000000
χ294444444444-4-4-4-4000000000000000000000000000000
χ3044444-4-4-4-44-4-444000000000000000000000000000000
χ314444-40000-4004i−4i00002-22-22i−2i2i−2i000000000000000000
χ324444-40000-4004i−4i0000-22-22−2i2i−2i2i000000000000000000
χ334444-40000-400−4i4i00002-22-2−2i2i−2i2i000000000000000000
χ344444-40000-400−4i4i0000-22-222i−2i2i−2i000000000000000000
χ3544-4-440000-44-4004-40000000000000000000000000000
χ3644-4-440000-44-400-440000000000000000000000000000
χ3744-4-4-44i4i−4i−4i4000000002i−2i−2i2i2-2-22000000000000000000
χ3844-4-4-44i4i−4i−4i400000000−2i2i2i−2i-222-2000000000000000000
χ3944-4-4-4−4i−4i4i4i4000000002i−2i−2i2i-222-2000000000000000000
χ4044-4-4-4−4i−4i4i4i400000000−2i2i2i−2i2-2-22000000000000000000
χ418-88i−8i04+4i−4−4i4−4i−4+4i00000000000000000000000000000000000
χ428-88i−8i0−4−4i4+4i−4+4i4−4i00000000000000000000000000000000000
χ438-8−8i8i04−4i−4+4i4+4i−4−4i00000000000000000000000000000000000
χ448-8−8i8i0−4+4i4−4i−4−4i4+4i00000000000000000000000000000000000

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