Finite Group Databasebeta

← Group #139331

Character table — Group #139331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11112222444444488888888888161616161616161616161616161616161616323232
order12222244444444422224448888224444448888888888488
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11-1-1
χ41111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111
χ511111111111-1-1-1-11-1-1-111-1ii−i−i111-1ii−i−i11i−i-1-1ii−i−i-1i−i
χ611111111111-1-1-1-11-1-1-111-1ii−i−i-1-11-1−i−iii-1-1i−i11ii−i−i1−ii
χ711111111111-1-1-1-11-1-1-111-1−i−iii111-1−i−iii11−ii-1-1−i−iii-1−ii
χ811111111111-1-1-1-11-1-1-111-1−i−iii-1-11-1ii−i−i-1-1−ii11−i−iii1i−i
χ911111111-1-1111111-1-111-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111
χ1011111111-1-1111111-1-111-111111-1-1-1-11111111111-1-1-1-1-1-1-1
χ1111111111-1-1111111-1-111-11-1-1-1-111-1-11111-1-1-1-1-1-111111-1-1
χ1211111111-1-1111111-1-111-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-111
χ1311111111-1-11-1-1-1-1111-11-1-1ii−i−i11-11−i−iii-1-1i−i11−i−iii-1i−i
χ1411111111-1-11-1-1-1-1111-11-1-1ii−i−i-1-1-11ii−i−i11i−i-1-1−i−iii1−ii
χ1511111111-1-11-1-1-1-1111-11-1-1−i−iii11-11ii−i−i-1-1−ii11ii−i−i-1−ii
χ1611111111-1-11-1-1-1-1111-11-1-1−i−iii-1-1-11−i−iii11−ii-1-1ii−i−i1i−i
χ172222222222222-2-2-2-2-22-22-2000000-2200000000000000000
χ1822222222222-2-222-222-2-222000000-2-200000000000000000
χ1922222222-2-2222-2-2-2222-2-2-20000002-200000000000000000
χ2022222222-2-22-2-222-2-2-2-2-2-220000002200000000000000000
χ21222222-2-200-22222-200-220-222220000000000-2-2000000000
χ22222222-2-200-22222-200-220-2-2-2-2-2000000000022000000000
χ23222222-2-200-222-2-2200-2-2020000000000000000002i−2i2i−2i000
χ24222222-2-200-222-2-2200-2-202000000000000000000−2i2i−2i2i000
χ25222222-2-200-2-2-2222002-20-20000000000000000002-2-22000
χ26222222-2-200-2-2-2222002-20-2000000000000000000-222-2000
χ27222222-2-200-2-2-2-2-2-20022022i2i−2i−2i0000000000−2i2i000000000
χ28222222-2-200-2-2-2-2-2-2002202−2i−2i2i2i00000000002i−2i000000000
χ294444-4-44444-4000000000-400000000000000000000000000
χ304444-4-444-4-4-4000000000400000000000000000000000000
χ314444-4-4-4-4004000004-400000000000000000000000000000
χ324444-4-4-4-400400000-4400000000000000000000000000000
χ3344-4-4004-44i−4i00000000000000002-20000002i−2i00000000000
χ3444-4-4004-44i−4i0000000000000000-22000000−2i2i00000000000
χ3544-4-4004-4−4i4i00000000000000002-2000000−2i2i00000000000
χ3644-4-4004-4−4i4i0000000000000000-220000002i−2i00000000000
χ374-44-44-4000004i−4i0000000002+2i−2−2i2−2i−2+2i000000000000000000000
χ384-44-44-4000004i−4i000000000−2−2i2+2i−2+2i2−2i000000000000000000000
χ394-44-44-400000−4i4i0000000002−2i−2+2i2+2i−2−2i000000000000000000000
χ404-44-44-400000−4i4i000000000−2+2i2−2i−2−2i2+2i000000000000000000000
χ414-44-4-4400000004-40000000000000002i−2i2i−2i0000000000000
χ424-44-4-4400000004-4000000000000000−2i2i−2i2i0000000000000
χ434-44-4-440000000-440000000000000002-2-220000000000000
χ444-44-4-440000000-44000000000000000-222-20000000000000
χ4588-8-800-88000000000000000000000000000000000000000
χ468-8-88000000000000000000000000000000000022−220000000
χ478-8-880000000000000000000000000000000000−22220000000

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