Finite Group Databasebeta

← Group #130615

Character table — Group #130615

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size111122224444444888888888888816161616161616161616161616161632323232
order12222244444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-111-11-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111-1-1-1-111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-11-1-1-1-1111111-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111-1-11-1-1-1-1111111-1-1-111-1-1-1-1-1-11111-1-111
χ7111111111111111-1-11-1-1-1-1-1-1-1-1111-11-1-1111111-1-1-1-1-1-111
χ8111111111111111-1-11-1-1-1-1-1-1-1-1111-11-1-111-1-1-1-1111111-1-1
χ911111111111-1-1-1-1111-1-1-1-11111-1-1-11-1-1-111ii−i−iii−i−ii−ii−i
χ1011111111111-1-1-1-1111-1-1-1-11111-1-1-11-1-1-111−i−iii−i−iii−ii−ii
χ1111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111-1-1ii−i−iii−i−i−ii−ii
χ1211111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111-1-1−i−iii−i−iiii−ii−i
χ1311111111111-1-1-1-1-1-1111111111-1-11-11-1-1-1-1ii−i−i−i−iiii−i−ii
χ1411111111111-1-1-1-1-1-1111111111-1-11-11-1-1-1-1−i−iiiii−i−i−iii−i
χ1511111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii−iii−i
χ1611111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-11111−i−iiiii−i−ii−i−ii
χ17222222222-2-222-2-200-2000022-2-22-20002-200000000000000
χ18222222222-2-222-2-200-20000-2-2222-2000-2200000000000000
χ19222222222-2-2-2-22200-2000022-2-2-22000-2200000000000000
χ20222222222-2-2-2-22200-20000-2-222-220002-200000000000000
χ21222222-2-2-222222222-222-2-20000-2-20-200000000000000000
χ22222222-2-2-2222222-2-2-2-2-2220000-2-20200000000000000000
χ23222222-2-2-222-2-2-2-222-2-2-2220000220-200000000000000000
χ24222222-2-2-222-2-2-2-2-2-2-222-2-20000220200000000000000000
χ25222222-2-2-2-2-222-2-200200000000-2220-2002-2000000000000
χ26222222-2-2-2-2-222-2-200200000000-22-20200-22000000000000
χ27222222-2-2-2-2-2-2-222002000000002-220-200-22000000000000
χ28222222-2-2-2-2-2-2-222002000000002-2-202002-2000000000000
χ292-22-2-220002-22i−2i2i−2i2-202i−2i0000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ302-22-2-220002-22i−2i2i−2i2-202i−2i000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ312-22-2-220002-22i−2i2i−2i-220−2i2i0000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ322-22-2-220002-22i−2i2i−2i-220−2i2i000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ332-22-2-220002-2−2i2i−2i2i2-20−2i2i0000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ342-22-2-220002-2−2i2i−2i2i2-20−2i2i000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ352-22-2-220002-2−2i2i−2i2i-2202i−2i0000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ362-22-2-220002-2−2i2i−2i2i-2202i−2i000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ374444-4-444-40000000000000004i−4i000000000000000000000
χ384444-4-444-4000000000000000−4i4i000000000000000000000
χ394444-4-4-4-4400000000000004i−4i00000000000000000000000
χ404444-4-4-4-440000000000000−4i4i00000000000000000000000
χ414-44-4-44000-444i−4i−4i4i00000000000000000000000000000000
χ424-44-4-44000-44−4i4i4i−4i00000000000000000000000000000000
χ4388-8-800000000000000004-40000000000000000000000000
χ4488-8-80000000000000000-440000000000000000000000000
χ458-88-88-800000000000000000000000000000000000000000
χ468-8-88008i−8i000000000000000000000000000000000000000
χ478-8-8800−8i8i000000000000000000000000000000000000000

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