Finite Group Databasebeta

← Group #129713

Character table — Group #129713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order1222222222444422444488882488888822224444444444441616161616161616
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
χ511111111111111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111-1-1-1-11111111-1-1111111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111-1-1-1-11111111-1-1111111-1-111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111-1-1-1-11111111-1-1111111-1-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ1211111-1-1-1-11111111-1-1111111-1-111-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ1311111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000
χ1822222222222222-2-222-2-22222-2-2-2-2-2-222000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-200002-200000000000000000000002−22−22−22−2
χ202222222222-2-2-2-222-2-2-2-200002-20000000000000000000000−22−22−22−22
χ212222222222-2-2-2-2-2-2-2-2220000-220000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ222222222222-2-2-2-2-2-2-2-2220000-220000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ2322222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2422222-2-2-2-222222-2-2-2-2-2-2222222-2-222-2-2000000000000000000000000
χ2522222-2-2-2-22-2-2-2-22222-2-20000-2200000000000000000000002−2−222−2−22
χ2622222-2-2-2-22-2-2-2-22222-2-20000-220000000000000000000000−222−2−222−2
χ2722222-2-2-2-22-2-2-2-2-2-2222200002-20000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ2822222-2-2-2-22-2-2-2-2-2-2222200002-20000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ292222-222-2-2-222-2-2002-2002i2i−2i−2i0000002i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ302222-222-2-2-222-2-2002-2002i2i−2i−2i0000002i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ312222-222-2-2-222-2-2002-200−2i−2i2i2i000000−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ322222-222-2-2-222-2-2002-200−2i−2i2i2i000000−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ332222-2-2-222-222-2-200-22002i2i−2i−2i000000−2i2i000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ342222-2-2-222-222-2-200-22002i2i−2i−2i000000−2i2i00000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ352222-2-2-222-222-2-200-2200−2i−2i2i2i0000002i−2i000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ362222-2-2-222-222-2-200-2200−2i−2i2i2i0000002i−2i00000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ372-2-22-2000022-2-222-2002-22-22-2002-20000002-2002-20000000000000000
χ382-2-22-2000022-2-222-2002-22-22-2002-2000000-2200-220000000000000000
χ392-2-22-2000022-2-222-2002-2-22-2200-2200002-2002-2000000000000000000
χ402-2-22-2000022-2-222-2002-2-22-2200-220000-2200-22000000000000000000
χ412-2-22-2000022-2-22-2200-222-22-200-2200002-200-22000000000000000000
χ422-2-22-2000022-2-22-2200-222-22-200-220000-22002-2000000000000000000
χ432-2-22-2000022-2-22-2200-22-22-22002-20000002-200-220000000000000000
χ442-2-22-2000022-2-22-2200-22-22-22002-2000000-22002-20000000000000000
χ454444-444-4-4-4-4-44400-4400000000000000000000000000000000000000
χ464444-4-4-444-4-4-444004-400000000000000000000000000000000000000
χ474-4-4440000-44-44-40000004i−4i−4i4i00000000000000000000000000000000
χ484-4-4440000-44-44-4000000−4i4i4i−4i00000000000000000000000000000000
χ494-4-4440000-4-44-44000000000000004-400000000000000000000000000
χ504-4-4440000-4-44-4400000000000000-4400000000000000000000000000
χ514-4-44-400004-444-44-400-44000000000000000000000000000000000000
χ524-4-44-400004-444-4-44004-4000000000000000000000000000000000000
χ5388-8-80008-800000000000000000000000000000000000000000000000
χ5488-8-8000-8800000000000000000000000000000000000000000000000
χ558-88-808-80000000000000000000000000000000000000000000000000
χ568-88-80-880000000000000000000000000000000000000000000000000

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