Finite Group Databasebeta

← Group #152243

Character table — Group #152243

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222222444488888888888888881616161616163232323232323232
order12222244444444444444448888888844444488888888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ511111111111111-1-11111-1-111111111-1-1-1-1-1-1ii−i−iii−i−i
χ611111111111111-1-11111-1-111111111-1-1-1-1-1-1−i−iii−i−iii
χ711111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ811111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ9111111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-11-11-11-11-1
χ10111111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-1-11-11-11-11
χ11111111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1111-11-1-11-11
χ12111111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111-11-111-11-1
χ13111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-111i−i−iii−i−ii
χ14111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-111−iii−i−iii−i
χ15111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1i−i−ii−iii−i
χ16111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1−iii−ii−i−ii
χ17222222222222222-2-2-2-2-22-2000000002-2000000000000
χ1822222222222222-22-2-2-2-2-2200000000-22000000000000
χ19222222-2-2-2-2-2-2222-2-2-2222-200000000-22000000000000
χ20222222-2-2-2-2-2-222-22-2-222-22000000002-2000000000000
χ212-22-22-20000002-2222-200-2-2000022-2-200002-200000000
χ222-22-22-20000002-2222-200-2-20000-2-2220000-2200000000
χ232-22-22-20000002-22-2-2200-222i2i−2i−2i0000002i−2i0000000000
χ242-22-22-20000002-22-2-2200-22−2i−2i2i2i000000−2i2i0000000000
χ252-22-22-20000002-2-22-22002-22i2i−2i−2i000000−2i2i0000000000
χ262-22-22-20000002-2-22-22002-2−2i−2i2i2i0000002i−2i0000000000
χ272-22-22-20000002-2-2-22-20022000022-2-20000-2200000000
χ282-22-22-20000002-2-2-22-200220000-2-22200002-200000000
χ294444444444-4-4-4-4000000000000000000000000000000
χ30444444-4-4-4-444-4-4000000000000000000000000000000
χ314444-4-444-4-40000000000002i−2i2i−2i2i−2i2i−2i00000000000000
χ324444-4-444-4-4000000000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ334444-4-4-4-4440000000000002i−2i2i−2i−2i2i−2i2i00000000000000
χ344444-4-4-4-444000000000000−2i2i−2i2i2i−2i2i−2i00000000000000
χ354-44-44-4000000-4400004i−4i000000000000000000000000
χ364-44-44-4000000-440000−4i4i000000000000000000000000
χ374-44-4-4400004i−4i00000000002-2-222i−2i−2i2i00000000000000
χ384-44-4-4400004i−4i0000000000-222-2−2i2i2i−2i00000000000000
χ394-44-4-440000−4i4i00000000002-2-22−2i2i2i−2i00000000000000
χ404-44-4-440000−4i4i0000000000-222-22i−2i−2i2i00000000000000
χ4188-8-800008-80000000000000000000000000000000000
χ4288-8-80000-880000000000000000000000000000000000
χ438-8-88008i−8i000000000000000000000000000000000000
χ448-8-8800−8i8i000000000000000000000000000000000000

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