Finite Group Databasebeta

← Group #347992

Character table — Group #347992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222444444444444444888888888888888888888816161616323232323232
order12222244444422224444444888822444444888888888888884444448888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-1
χ611111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1111-1-1
χ9111111111111-1-1-1-1111-1-1-1-111111-11-11-11-11111-1-1-1-1-1-111-1-11111-1-11-11-1
χ10111111111111-1-1-1-1111-1-1-1-111111-11-11-11-11111-1-1-1-1-1-111-1-1-1-1-1-111-11-11
χ11111111111111-1-1-1-1111-1-1-1-11111-11-11-11-1111-1-111-1-1-1-1-1-1111111-1-1-11-11
χ12111111111111-1-1-1-1111-1-1-1-11111-11-11-11-1111-1-111-1-1-1-1-1-111-1-1-1-1111-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-11-11-11-11-1-1-1-1-1111111-1-11111-1-1-111-1-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-11-11-11-11-1-1-1-1-1111111-1-111-1-1111-1-111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-11-11-11-11-1-111-1-1111111-1-111-1-1-11-111-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-11-11-11-11-1-111-1-1111111-1-1-1-1111-11-1-11
χ1722222222-222-22222-2-2-2-2-2-2-2000022-2-222-2-2000000000000000000000000
χ1822222222-222-22222-2-2-2-2-2-2-20000-2-222-2-222000000000000000000000000
χ1922222222-222-2-2-2-2-2-2-2-2222200002-2-222-2-22000000000000000000000000
χ2022222222-222-2-2-2-2-2-2-2-222220000-222-2-222-2000000000000000000000000
χ21222222-2-22-2-2222-2-2-2-2222-2-2222200000000-2-2000022-2-200000000000000
χ22222222-2-22-2-2222-2-2-2-2222-2-2-2-2-2-200000000220000-2-22200000000000000
χ23222222-2-22-2-22-2-222-2-22-2-222222200000000-2-20000-2-22200000000000000
χ24222222-2-22-2-22-2-222-2-22-2-222-2-2-2-20000000022000022-2-200000000000000
χ25222222-2-2-2-2-2-222-2-222-2-2-222000000000000002i−2i2i−2i00002i−2i2i−2i0000000000
χ26222222-2-2-2-2-2-222-2-222-2-2-22200000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000
χ27222222-2-2-2-2-2-2-2-22222-222-2-2000000000000002i−2i−2i2i00002i−2i−2i2i0000000000
χ28222222-2-2-2-2-2-2-2-22222-222-2-200000000000000−2i2i2i−2i0000−2i2i2i−2i0000000000
χ292222-2-22-222-2200002-2-2000022-2-2020-20-2022-20022000000-2-20000000000
χ302222-2-22-222-2200002-2-2000022-2-20-202020-22-200-2-2000000220000000000
χ312222-2-22-222-2200002-2-20000-2-222020-20-202-2200-2-2000000220000000000
χ322222-2-22-222-2200002-2-20000-2-2220-202020-2-220022000000-2-20000000000
χ332222-2-22-2-22-2-20000-2220000000002020-20-2002i−2i002i−2i2i−2i−2i2i000000000000
χ342222-2-22-2-22-2-20000-2220000000002020-20-200−2i2i00−2i2i−2i2i2i−2i000000000000
χ352222-2-22-2-22-2-20000-222000000000-20-20202002i−2i00−2i2i−2i2i−2i2i000000000000
χ362222-2-22-2-22-2-20000-222000000000-20-2020200−2i2i002i−2i2i−2i2i−2i000000000000
χ372222-2-2-222-2220000-22-2000022-2-220-20-2020-2222000000-2-2000000000000
χ382222-2-2-222-2220000-22-2000022-2-2-202020-20-22-2-200000022000000000000
χ392222-2-2-222-2220000-22-20000-2-22220-20-20202-2-2-200000022000000000000
χ402222-2-2-222-2220000-22-20000-2-222-202020-202-222000000-2-2000000000000
χ412222-2-2-22-2-22-200002-22000000002020-20-2000002i−2i2i−2i−2i2i00−2i2i0000000000
χ422222-2-2-22-2-22-200002-22000000002020-20-200000−2i2i−2i2i2i−2i002i−2i0000000000
χ432222-2-2-22-2-22-200002-2200000000-20-20202000002i−2i−2i2i2i−2i00−2i2i0000000000
χ442222-2-2-22-2-22-200002-2200000000-20-2020200000−2i2i2i−2i−2i2i002i−2i0000000000
χ454-44-44-4440-4-404-44-40000000000000000000000000000000000000000000
χ464-44-44-4440-4-40-44-440000000000000000000000000000000000000000000
χ474-44-44-4-4-404404-4-440000000000000000000000000000000000000000000
χ484-44-44-4-4-40440-444-40000000000000000000000000000000000000000000
χ494-44-4-444-40-44000000004i−4i4i−4i000000000000000000000000000000000000
χ504-44-4-444-40-4400000000−4i4i−4i4i000000000000000000000000000000000000
χ514-44-4-44-4404-4000000004i−4i−4i4i000000000000000000000000000000000000
χ524-44-4-44-4404-400000000−4i4i4i−4i000000000000000000000000000000000000
χ534-4-440000400-400000000000004i−4i00000000000000000000002i−2i2-2000000
χ544-4-440000400-400000000000004i−4i0000000000000000000000−2i2i-22000000
χ554-4-440000400-40000000000000−4i4i00000000000000000000002i−2i-22000000
χ564-4-440000400-40000000000000−4i4i0000000000000000000000−2i2i2-2000000
χ5788-8-8000000000000000000042−420000000000000000000000000000000000
χ5888-8-80000000000000000000−42420000000000000000000000000000000000
χ598-8-880000-800800000000000000000000000000000000000000000000000

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