Finite Group Databasebeta

← Group #129757

Character table — Group #129757

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444444444888888161616161616161616161616161616161616161616161616
order12222222222222222244444444444444224444444444444488888888
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
χ511111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11-11-111-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11-11-111-1-1-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-11-11-1-11111-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-11-11-1-111-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-11-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-11-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-11-1111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-11-1111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222000000000000000000000000
χ1822222222222222-2-2-2-222222222-2-2-2-2-2-2000000000000000000000000
χ192222222222-2-2-2-222222222-2-2-2-2-2-222-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222000000000000000000000000
χ2122222-2-2-2-2200002-22-2000022-2-22-20000020-2002-20000000000000000
χ2222222-2-2-2-2200002-22-2000022-2-22-200000-20200-220000000000000000
χ2322222-2-2-2-2200002-22-20000-2-222-22000020-202-2000000000000000000
χ2422222-2-2-2-2200002-22-20000-2-222-220000-2020-22000000000000000000
χ2522222-2-2-2-220000-22-22000022-2-2-22000020-20-22000000000000000000
χ2622222-2-2-2-220000-22-22000022-2-2-220000-20202-2000000000000000000
χ2722222-2-2-2-220000-22-220000-2-2222-20000020-200-220000000000000000
χ2822222-2-2-2-220000-22-220000-2-2222-200000-202002-20000000000000000
χ292-22-2222-2-2-222-2-200002i2i−2i−2i2i−2i2i−2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ302-22-2222-2-2-222-2-200002i2i−2i−2i2i−2i2i−2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ312-22-2222-2-2-222-2-20000−2i−2i2i2i−2i2i−2i2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ322-22-2222-2-2-222-2-20000−2i−2i2i2i−2i2i−2i2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ332-22-2222-2-2-2-2-22200002i2i−2i−2i−2i2i−2i2i000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ342-22-2222-2-2-2-2-22200002i2i−2i−2i−2i2i−2i2i00000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ352-22-2222-2-2-2-2-2220000−2i−2i2i2i2i−2i2i−2i000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ362-22-2222-2-2-2-2-2220000−2i−2i2i2i2i−2i2i−2i00000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ372-22-2-22-22-222-22-222-2-20000000000002-20000000000000000i2−i2i2−i2i2−i2i2−i2
χ382-22-2-22-22-222-22-222-2-20000000000002-20000000000000000−i2i2−i2i2−i2i2−i2i2
χ392-22-2-22-22-222-22-2-2-222000000000000-2200000000000000002−22−2−22−22
χ402-22-2-22-22-222-22-2-2-222000000000000-220000000000000000−22−222−22−2
χ412-22-2-22-22-22-22-2222-2-2000000000000-220000000000000000i2−i2−i2i2i2−i2−i2i2
χ422-22-2-22-22-22-22-2222-2-2000000000000-220000000000000000−i2i2i2−i2−i2i2i2−i2
χ432-22-2-22-22-22-22-22-2-2220000000000002-200000000000000002−2−22−222−2
χ442-22-2-22-22-22-22-22-2-2220000000000002-20000000000000000−222−22−2−22
χ454444-44-4-44-44-4-44000000000000000000000000000000000000000000
χ464444-44-4-44-4-444-4000000000000000000000000000000000000000000
χ474444-4-444-4-40000000000000000004-400000000000000000000000000
χ484444-4-444-4-4000000000000000000-4400000000000000000000000000
χ494-44-44-4-444-40000000000004i−4i−4i4i000000000000000000000000000000
χ504-44-44-4-444-4000000000000−4i4i4i−4i000000000000000000000000000000
χ514-44-4-4-44-44400004-4-4400000000000000000000000000000000000000
χ524-44-4-4-44-4440000-444-400000000000000000000000000000000000000
χ5388-8-8000000000000004i−4i4i−4i0000000000000000000000000000000000
χ5488-8-800000000000000−4i4i−4i4i0000000000000000000000000000000000
χ558-8-88000000000000004-4-440000000000000000000000000000000000
χ568-8-8800000000000000-444-40000000000000000000000000000000000

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