Finite Group Databasebeta

← Group #138039

Character table — Group #138039

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222-2-22222-2-2-2-222-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-222000000000000000000000000
χ19222222222222-2-2-2-222222222-2-2-2-2-2-222000000000000000000000000
χ20222222222222-2-2-2-222-2-2-2-2222222-2-2-2-2000000000000000000000000
χ2122-2-222-2-22-22-200002i−2i00002i−2i2i−2i2-20000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ2222-2-222-2-22-22-200002i−2i00002i−2i2i−2i2-2000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ2322-2-222-2-22-22-200002i−2i00002i−2i−2i2i-220000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ2422-2-222-2-22-22-200002i−2i00002i−2i−2i2i-22000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ2522-2-222-2-22-22-20000−2i2i0000−2i2i2i−2i-220000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ2622-2-222-2-22-22-20000−2i2i0000−2i2i2i−2i-22000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ2722-2-222-2-22-22-20000−2i2i0000−2i2i−2i2i2-20000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ2822-2-222-2-22-22-20000−2i2i0000−2i2i−2i2i2-2000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ292-2-2-22-222-222-22-22-2220000-2-200002-20000000000000000002i−2i2i−2i0000
χ302-2-2-22-222-222-22-22-2220000-2-200002-2000000000000000000−2i2i−2i2i0000
χ312-2-2-22-222-222-22-22-2-2-20000220000-2200000000000000000000002-22-2
χ322-2-2-22-222-222-22-22-2-2-20000220000-220000000000000000000000-22-22
χ332-2-2-22-222-222-2-22-22220000-2-20000-2200000000000000000000002i−2i−2i2i
χ342-2-2-22-222-222-2-22-22220000-2-20000-220000000000000000000000−2i2i2i−2i
χ352-2-2-22-222-222-2-22-22-2-200002200002-20000000000000000002-2-220000
χ362-2-2-22-222-222-2-22-22-2-200002200002-2000000000000000000-222-20000
χ3744444444-4-4-4-400000044-4-40000000000000000000000000000000000
χ3844444444-4-4-4-4000000-4-4440000000000000000000000000000000000
χ39444-4-4-4-440000000000004i−4i00000000002i−2i2-200000000000000000000
χ40444-4-4-4-440000000000004i−4i0000000000−2i2i-2200000000000000000000
χ41444-4-4-4-44000000000000−4i4i00000000002i−2i-2200000000000000000000
χ42444-4-4-4-44000000000000−4i4i0000000000−2i2i2-200000000000000000000
χ4344-4-444-4-4-44-4444-4-40000000000000000000000000000000000000000
χ4444-4-444-4-4-44-44-4-4440000000000000000000000000000000000000000
χ454-4444-4-4-444-4-44-4-440000000000000000000000000000000000000000
χ464-4444-4-4-444-4-4-444-40000000000000000000000000000000000000000
χ474-4444-4-4-4-4-44400004i−4i0000−4i4i00000000000000000000000000000000
χ484-4444-4-4-4-4-4440000−4i4i00004i−4i00000000000000000000000000000000
χ494-44-4-444-400000000004i−4i00000000000000002-22i−2i0000000000000000
χ504-44-4-444-400000000004i−4i0000000000000000-22−2i2i0000000000000000
χ514-44-4-444-40000000000−4i4i00000000000000002-2−2i2i0000000000000000
χ524-44-4-444-40000000000−4i4i0000000000000000-222i−2i0000000000000000
χ534-4-4-44-4444-4-440000000000000000004-4000000000000000000000000
χ544-4-4-44-4444-4-44000000000000000000-44000000000000000000000000
χ5588-88-8-88-8000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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