Finite Group Databasebeta

← Group #8577

Character table — Group #8577

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111111122222222222244444444888888888888888888888888
order1222222222224444444444444444224444444444444488888888
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-22222-2-2-2-2-2-2-2-222000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000
χ1922222222-2-2-2-222222222-2-2-2-222-2-2000000000000000000000000
χ2022222222-2-2-2-222-2-2-2-222-2-222-2-222000000000000000000000000
χ2122-222-2-2-200002i−2i2i2i−2i−2i2i−2i00002-200000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ2222-222-2-2-200002i−2i2i2i−2i−2i2i−2i00002-20000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ2322-222-2-2-200002i−2i−2i−2i2i2i2i−2i0000-2200000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ2422-222-2-2-200002i−2i−2i−2i2i2i2i−2i0000-220000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ2522-222-2-2-20000−2i2i2i2i−2i−2i−2i2i0000-2200000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ2622-222-2-2-20000−2i2i2i2i−2i−2i−2i2i0000-220000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ2722-222-2-2-20000−2i2i−2i−2i2i2i−2i2i00002-200000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ2822-222-2-2-20000−2i2i−2i−2i2i2i−2i2i00002-20000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ2922-2-2-222-222-2-2220000-2-22-20000002-22-200000000000000000000
χ3022-2-2-222-222-2-2220000-2-22-2000000-22-2200000000000000000000
χ3122-2-2-222-222-2-2-2-2000022-2200000000002i−2i2i−2i0000000000000000
χ3222-2-2-222-222-2-2-2-2000022-220000000000−2i2i−2i2i0000000000000000
χ3322-2-2-222-2-2-222220000-2-2-2200000000002i−2i−2i2i0000000000000000
χ3422-2-2-222-2-2-222220000-2-2-220000000000−2i2i2i−2i0000000000000000
χ3522-2-2-222-2-2-222-2-20000222-20000002-2-2200000000000000000000
χ3622-2-2-222-2-2-222-2-20000222-2000000-222-200000000000000000000
χ372-2-22-22-222-22-2002-22-2000000002-20000000000000000i2−i2i2−i2i2−i2i2−i2
χ382-2-22-22-222-22-2002-22-2000000002-20000000000000000−i2i2−i2i2−i2i2−i2i2
χ392-2-22-22-222-22-200-22-2200000000-220000000000000000i2−i2i2−i2−i2i2−i2i2
χ402-2-22-22-222-22-200-22-2200000000-220000000000000000−i2i2−i2i2i2−i2i2−i2
χ412-2-22-22-22-22-22002-22-200000000-2200000000000000002−2−222−2−22
χ422-2-22-22-22-22-22002-22-200000000-220000000000000000−222−2−222−2
χ432-2-22-22-22-22-2200-22-22000000002-200000000000000002−2−22−222−2
χ442-2-22-22-22-22-2200-22-22000000002-20000000000000000−222−22−2−22
χ45444-4-4-4-4400004i−4i0000−4i4i00000000000000000000000000000000
χ46444-4-4-4-440000−4i4i00004i−4i00000000000000000000000000000000
χ474-444-4-44-40000004i−4i−4i4i0000000000000000000000000000000000
χ484-444-4-44-4000000−4i4i4i−4i0000000000000000000000000000000000
χ494-44-444-4-44-4-440000000000000000000000000000000000000000
χ504-44-444-4-4-444-40000000000000000000000000000000000000000
χ514-4-4-44-444000000000000004-40000000000000000000000000000
χ524-4-4-44-44400000000000000-440000000000000000000000000000

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