Finite Group Databasebeta

← Group #152249

Character table — Group #152249

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222222444488888888888888881616161616163232323232323232
order12442488882488224444444488888844888888888888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111-1-1111111-1-1111111-1-1-1-1-1-1ii−i−iii−i−i
χ611111111111111-1-1111111-1-1111111-1-1-1-1-1-1−i−iii−i−iii
χ711111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1ii−i−i−i−iii
χ811111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1−i−iiiii−i−i
χ9111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-111-1-11-11-11-11-1
χ10111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-111-1-1-11-11-11-11
χ11111111-1-1-1-111-1-11111-1-1-1-111-1-1111111-1-1-1-11-11-1-11-11
χ12111111-1-1-1-111-1-11111-1-1-1-111-1-1111111-1-1-1-1-11-111-11-1
χ13111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111i−i−iii−i−ii
χ14111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111−iii−i−iii−i
χ15111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111i−i−ii−iii−i
χ16111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111−iii−ii−i−ii
χ17222222222222222-2-2-200002-2-2-2000000002-200000000
χ1822222222222222-22-2-20000-22-2-200000000-2200000000
χ19222222-2-2-2-222-2-22-2-2-200002-22200000000-2200000000
χ20222222-2-2-2-222-2-2-22-2-20000-2222000000002-200000000
χ2122-2-22-20000-2200222-20000-2-20022-2-22-2000000000000
χ2222-2-22-20000-2200222-20000-2-200-2-222-22000000000000
χ2322-2-22-20000-22002-2-222i2i−2i−2i-22000000002i−2i0000000000
χ2422-2-22-20000-22002-2-22−2i−2i2i2i-2200000000−2i2i0000000000
χ2522-2-22-20000-2200-22-222i2i−2i−2i2-200000000−2i2i0000000000
χ2622-2-22-20000-2200-22-22−2i−2i2i2i2-2000000002i−2i0000000000
χ2722-2-22-20000-2200-2-22-20000220022-2-2-22000000000000
χ2822-2-22-20000-2200-2-22-200002200-2-2222-2000000000000
χ294444444444-4-4-4-4000000000000000000000000000000
χ30444444-4-4-4-4-4-444000000000000000000000000000000
χ314444-4-40000004i−4i00002-22-200002i−2i2i−2i00000000000000
χ324444-4-40000004i−4i0000-22-220000−2i2i−2i2i00000000000000
χ334444-4-4000000−4i4i00002-22-20000−2i2i−2i2i00000000000000
χ344444-4-4000000−4i4i0000-22-2200002i−2i2i−2i00000000000000
χ3544-4-44-400004-40000000000004i−4i000000000000000000
χ3644-4-44-400004-4000000000000−4i4i000000000000000000
χ3744-4-4-4444-4-4000000002i−2i−2i2i00002i−2i−2i2i00000000000000
χ3844-4-4-4444-4-400000000−2i2i2i−2i0000−2i2i2i−2i00000000000000
χ3944-4-4-44-4-444000000002i−2i−2i2i0000−2i2i2i−2i00000000000000
χ4044-4-4-44-4-44400000000−2i2i2i−2i00002i−2i−2i2i00000000000000
χ418-88i−8i004i2−4i242−420000000000000000000000000000000000
χ428-88i−8i00−4i24i2−42420000000000000000000000000000000000
χ438-8−8i8i004i2−4i2−42420000000000000000000000000000000000
χ448-8−8i8i00−4i24i242−420000000000000000000000000000000000

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