Finite Group Databasebeta

← Group #459754

Character table — Group #459754

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222222888888888888888816161616161616161616161616161616161616161616
order12222222224444444422444444888888882244444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111
χ311111111111111111111111111-1-1-1-1-1-1-1-111-111-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-111-1-1
χ51111111111111111111111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-111111111-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ9111111111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ11111111111111111111-1-1-1-11111-1-1-1-1111111-111-111-1-111-1-1-1-1-1-111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-11-1-111111-1-111-1-111-1-1-1-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11111111-1-111-1-1-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-111-1-1-1-111111111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-111
χ1722222-22-2-2-222-2-222-2-222-2-200000000000000000000002i−2i2i−2i00000000
χ1822222-22-2-2-222-2-222-2-222-2-20000000000000000000000−2i2i−2i2i00000000
χ1922222-22-2-2-222-2-222-2-2-2-22200000000000000000000002i−2i−2i2i00000000
χ2022222-22-2-2-222-2-222-2-2-2-2220000000000000000000000−2i2i2i−2i00000000
χ212222-22-2-2-22222-2-2-22-2000022-2-200002i2i−2i−2i0000002i−2i00000000000000
χ222222-22-2-2-22222-2-2-22-2000022-2-20000−2i−2i2i2i000000−2i2i00000000000000
χ232222-22-2-2-22222-2-2-22-20000-2-22200002i2i−2i−2i000000−2i2i00000000000000
χ242222-22-2-2-22222-2-2-22-20000-2-2220000−2i−2i2i2i0000002i−2i00000000000000
χ252222-22-2-2-22-2-2-2222-220000000022-2-200002-2200-20000000000000000
χ262222-22-2-2-22-2-2-2222-220000000022-2-20000-22-20020000000000000000
χ272222-22-2-2-22-2-2-2222-2200000000-2-22200002-2-20020000000000000000
χ282222-22-2-2-22-2-2-2222-2200000000-2-2220000-22200-20000000000000000
χ292-22-222-22-2-22-22-22-2-222-22-20000000000000002i−2i0002i−2i000000000000
χ302-22-222-22-2-22-22-22-2-222-22-2000000000000000−2i2i000−2i2i000000000000
χ312-22-222-22-2-22-22-22-2-22-22-220000000000000002i−2i000−2i2i000000000000
χ322-22-222-22-2-22-22-22-2-22-22-22000000000000000−2i2i0002i−2i000000000000
χ332-22-22-2-2-2222-2-222-22-22-2-2200002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ342-22-22-2-2-2222-2-222-22-22-2-220000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ352-22-22-2-2-2222-2-222-22-2-222-200002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ362-22-22-2-2-2222-2-222-22-2-222-20000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ372-22-2-2-222-222-2-2-2-22220000000000002-2-22000000000000002-200002-2
χ382-22-2-2-222-222-2-2-2-22220000000000002-2-2200000000000000-220000-22
χ392-22-2-2-222-222-2-2-2-2222000000000000-222-2000000000000002-20000-22
χ402-22-2-2-222-222-2-2-2-2222000000000000-222-200000000000000-2200002-2
χ412-22-2-2-222-22-22222-2-2-2000000002i−2i−2i2i000000000000000000002-22i−2i00
χ422-22-2-2-222-22-22222-2-2-2000000002i−2i−2i2i00000000000000000000-22−2i2i00
χ432-22-2-2-222-22-22222-2-2-200000000−2i2i2i−2i000000000000000000002-2−2i2i00
χ442-22-2-2-222-22-22222-2-2-200000000−2i2i2i−2i00000000000000000000-222i−2i00
χ454444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000
χ4644444-44-4-4-4-4-444-4-44400000000000000000000000000000000000000
χ474444-4-4-444-444-44-4-4-4400000000000000000000000000000000000000
χ484444-4-4-444-4-4-44-4444-400000000000000000000000000000000000000
χ494-44-444-44-4-4-44-44-444-400000000000000000000000000000000000000
χ504-44-44-4-4-444-444-4-44-4400000000000000000000000000000000000000
χ514-44-4-444-44-44-444-44-4-400000000000000000000000000000000000000
χ524-44-4-444-44-4-44-4-44-44400000000000000000000000000000000000000
χ5388-8-8000000000000000000004i−4i000000000000000000000000000000
χ5488-8-800000000000000000000−4i4i000000000000000000000000000000
χ558-8-880000000000000000004-400000000000000000000000000000000
χ568-8-88000000000000000000-4400000000000000000000000000000000

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