Finite Group Databasebeta

← Group #7634

Character table — Group #7634

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111111122222222222244444444888888888888888888888888
order1222222244444444444422444444444444448888888888888888
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
χ5111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-1-1-111111111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-222-2-2-2-2-2-222000000000000000000000000
χ18222222222222-2-22222-2-222-2-2-2-2-2-2000000000000000000000000
χ1922222222-2-2-2-222-2-2-2-22222-2-222-2-2000000000000000000000000
χ2022222222-2-2-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000
χ2122-22-2-22-200002i−2i2i2i−2i−2i2i−2i002-20000002i−2i002-20000000000000000
χ2222-22-2-22-200002i−2i2i2i−2i−2i2i−2i002-2000000−2i2i00-220000000000000000
χ2322-22-2-22-200002i−2i−2i−2i2i2i2i−2i00-2200002-2002i−2i000000000000000000
χ2422-22-2-22-200002i−2i−2i−2i2i2i2i−2i00-220000-2200−2i2i000000000000000000
χ2522-22-2-22-20000−2i2i2i2i−2i−2i−2i2i00-2200002-200−2i2i000000000000000000
χ2622-22-2-22-20000−2i2i2i2i−2i−2i−2i2i00-220000-22002i−2i000000000000000000
χ2722-22-2-22-20000−2i2i−2i−2i2i2i−2i2i002-20000002i−2i00-220000000000000000
χ2822-22-2-22-20000−2i2i−2i−2i2i2i−2i2i002-2000000−2i2i002-20000000000000000
χ2922-2-22-2-222i2i−2i−2i002i−2i2i−2i002-200000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ3022-2-22-2-222i2i−2i−2i002i−2i2i−2i002-20000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ3122-2-22-2-222i2i−2i−2i00−2i2i−2i2i00-2200000000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i
χ3222-2-22-2-222i2i−2i−2i00−2i2i−2i2i00-220000000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i
χ3322-2-22-2-22−2i−2i2i2i002i−2i2i−2i00-2200000000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i
χ3422-2-22-2-22−2i−2i2i2i002i−2i2i−2i00-220000000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i
χ3522-2-22-2-22−2i−2i2i2i00−2i2i−2i2i002-200000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ3622-2-22-2-22−2i−2i2i2i00−2i2i−2i2i002-20000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ372-2-2222-2-22-22-22i−2i0000−2i2i0000002i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ382-2-2222-2-22-22-22i−2i0000−2i2i0000002i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ392-2-2222-2-22-22-2−2i2i00002i−2i000000−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ402-2-2222-2-22-22-2−2i2i00002i−2i000000−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ412-2-2222-2-2-22-222i−2i0000−2i2i000000−2i2i000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ422-2-2222-2-2-22-222i−2i0000−2i2i000000−2i2i00000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ432-2-2222-2-2-22-22−2i2i00002i−2i0000002i−2i000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ442-2-2222-2-2-22-22−2i2i00002i−2i0000002i−2i00000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ45444-4-44-4-40000004-4-440000000000000000000000000000000000
χ46444-4-44-4-4000000-444-40000000000000000000000000000000000
χ474-444-4-4-440000440000-4-400000000000000000000000000000000
χ484-444-4-4-440000-4-400004400000000000000000000000000000000
χ494-44-44-44-44i−4i−4i4i0000000000000000000000000000000000000000
χ504-44-44-44-4−4i4i4i−4i0000000000000000000000000000000000000000
χ514-4-4-4-444400000000000000004-400000000000000000000000000
χ524-4-4-4-44440000000000000000-4400000000000000000000000000

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