Finite Group Databasebeta

← Group #130652

Character table — Group #130652

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size111122224444444888888888888816161616161616161616161616161632323232
order12222244224444422222224444444444444444488888888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-111-1-1-1-1111-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111-1-1-1-1111111111-1-1-1-11-1-111111111-1-1-1-1
χ6111111111111111-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111-1-1-1-1-1-111-1-1-1-11-1-111-1111111-1-1-1-1-1-111
χ8111111111111111-1-1-1-1-1-111-1-1-1-11-1-111-111-1-1-1-1111111-1-1
χ911111111111-1-1-1-1111111-1111-1-1-1-1-111-1-1-1ii−i−iii−i−ii−ii−i
χ1011111111111-1-1-1-1111111-1111-1-1-1-1-111-1-1-1−i−iii−i−iii−ii−ii
χ1111111111111-1-1-1-11111-1-1-11-1-111-1-1-1-1-1111ii−i−i−i−iiii−i−ii
χ1211111111111-1-1-1-11111-1-1-11-1-111-1-1-1-1-1111−i−iiiii−i−i−iii−i
χ1311111111111-1-1-1-1-1-1-1-111-1111-1-1-111-1-1-111ii−i−iii−i−i−ii−ii
χ1411111111111-1-1-1-1-1-1-1-111-1111-1-1-111-1-1-111−i−iii−i−iiii−ii−i
χ1511111111111-1-1-1-1-1-1-1-1-1-1-11-1-111-111111-1-1ii−i−i−i−iii−iii−i
χ1611111111111-1-1-1-1-1-1-1-1-1-1-11-1-111-111111-1-1−i−iiiii−i−ii−i−ii
χ1722222222-2-2222-2-222-2-2002-20000-22-200000000000000000
χ1822222222-2-2222-2-2-2-222002-20000-2-2200000000000000000
χ1922222222-2-22-2-22222-2-200-2-200002-2200000000000000000
χ2022222222-2-22-2-222-2-22200-2-2000022-200000000000000000
χ21222222-2-222-22222000022-2-2-2-2-2-2-20000200000000000000
χ22222222-2-222-222220000-2-2-2-22222-20000-200000000000000
χ23222222-2-222-2-2-2-2-20000222-2-2-22220000-200000000000000
χ24222222-2-222-2-2-2-2-20000-2-22-222-2-220000200000000000000
χ25222222-2-2-2-2-222-2-2000000-2200002002-202-2000000000000
χ26222222-2-2-2-2-222-2-2000000-220000200-220-22000000000000
χ27222222-2-2-2-2-2-2-222000000220000-2002-20-22000000000000
χ28222222-2-2-2-2-2-2-222000000220000-200-2202-2000000000000
χ2922-2-2-22002-202i−2i2i−2i000000002i−2i2-2000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ3022-2-2-22002-202i−2i2i−2i000000002i−2i2-200000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ3122-2-2-22002-202i−2i2i−2i00000000−2i2i-22000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000
χ3222-2-2-22002-202i−2i2i−2i00000000−2i2i-2200000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000
χ3322-2-2-22002-20−2i2i−2i2i000000002i−2i-22000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000
χ3422-2-2-22002-20−2i2i−2i2i000000002i−2i-2200000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000
χ3522-2-2-22002-20−2i2i−2i2i00000000−2i2i2-2000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ3622-2-2-22002-20−2i2i−2i2i00000000−2i2i2-200000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ374444-4-44400-40000004-40000000000000000000000000000
χ384444-4-44400-4000000-440000000000000000000000000000
χ394444-4-4-4-400400004-4000000000000000000000000000000
χ404444-4-4-4-40040000-44000000000000000000000000000000
χ4144-4-4-4400-4404i−4i−4i4i00000000000000000000000000000000
χ4244-4-4-4400-440−4i4i4i−4i00000000000000000000000000000000
χ4388-8-88-800000000000000000000000000000000000000000
χ448-88-80000000000000004-400000000000000000000000000
χ458-88-8000000000000000-4400000000000000000000000000
χ468-8-88008-8000000000000000000000000000000000000000
χ478-8-8800-88000000000000000000000000000000000000000

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