Finite Group Databasebeta

← Group #124652

Character table — Group #124652

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order1222222222444444444488884488888844444444888888881616161616161616
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
χ192222222222-2-2-2-222-2-2-2-200002-20000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ202222222222-2-2-2-222-2-2-2-200002-20000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ212222222222-2-2-2-2-2-2-2-2220000-2200000000000000000000002−22−2−22−22
χ222222222222-2-2-2-2-2-2-2-2220000-220000000000000000000000−22−222−22−2
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
χ2522222-2-2-2-22-2-2-2-22222-2-20000-220000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ2622222-2-2-2-22-2-2-2-22222-2-20000-220000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ2722222-2-2-2-22-2-2-2-2-2-2222200002-200000000000000000000002−2−22−222−2
χ2822222-2-2-2-22-2-2-2-2-2-2222200002-20000000000000000000000−222−22−2−22
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
χ372-2-2220000-22-22-22i−2i002i−2i2i−2i2i−2i002-20000002-2002i−2i0000000000000000
χ382-2-2220000-22-22-22i−2i002i−2i2i−2i2i−2i002-2000000-2200−2i2i0000000000000000
χ392-2-2220000-22-22-22i−2i002i−2i−2i2i−2i2i00-2200002-2002i−2i000000000000000000
χ402-2-2220000-22-22-22i−2i002i−2i−2i2i−2i2i00-220000-2200−2i2i000000000000000000
χ412-2-2220000-22-22-2−2i2i00−2i2i2i−2i2i−2i00-2200002-200−2i2i000000000000000000
χ422-2-2220000-22-22-2−2i2i00−2i2i2i−2i2i−2i00-220000-22002i−2i000000000000000000
χ432-2-2220000-22-22-2−2i2i00−2i2i−2i2i−2i2i002-20000002-200−2i2i0000000000000000
χ442-2-2220000-22-22-2−2i2i00−2i2i−2i2i−2i2i002-2000000-22002i−2i0000000000000000
χ454444-444-4-4-4-4-44400-4400000000000000000000000000000000000000
χ464444-4-4-444-4-4-444004-400000000000000000000000000000000000000
χ474-4-4440000-4-44-444i−4i00−4i4i000000000000000000000000000000000000
χ484-4-4440000-4-44-44−4i4i004i−4i000000000000000000000000000000000000
χ494-4-44-4000044-4-440000004-4-4400000000000000000000000000000000
χ504-4-44-4000044-4-44000000-444-400000000000000000000000000000000
χ514-4-44-400004-444-4000000000000004-400000000000000000000000000
χ524-4-44-400004-444-400000000000000-4400000000000000000000000000
χ5388-8-80008-800000000000000000000000000000000000000000000000
χ5488-8-8000-8800000000000000000000000000000000000000000000000
χ558-88-808-80000000000000000000000000000000000000000000000000
χ568-88-80-880000000000000000000000000000000000000000000000000

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