Finite Group Databasebeta

← Group #72310539

Character table — Group #72310539

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222444444881616161616161632323232323232323232323232323232326464646464646464646464646464646464128128
order12222222222222222444224444444444444444444444444444888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-11-11111-1-111-1-1-1-11-1-11-1-11111-1-1-1-11111-1-1
χ4111111111111111111111-11-11111-1-111-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111-11-1111-1-1-1-1-1-111-1-11-11-11-111111111-1-1-1-1-1-1
χ611111111111111111111-11-1111-1-1-1-1-1-111-1-11-11-11-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-11-1-1-1-111111111-1-1
χ91111111111111-1-1-1-11-1-1111111-1-111-1-1-1-1-1-1-1-1-1111ii−i−iii−i−iii−i−ii−i
χ101111111111111-1-1-1-11-1-1111111-1-111-1-1-1-1-1-1-1-1-1111−i−iii−i−iii−i−iii−ii
χ111111111111111-1-1-1-11-1-11-11-111-1-1-1-1-1-11111-1111-1-1ii−i−i−i−iiiii−i−i−ii
χ121111111111111-1-1-1-11-1-11-11-111-1-1-1-1-1-11111-1111-1-1−i−iiiii−i−i−i−iiii−i
χ131111111111111-1-1-1-11-1-1-11-111111-1-111-1-111-11-1-11-1ii−i−iii−i−i−i−iii−ii
χ141111111111111-1-1-1-11-1-1-11-111111-1-111-1-111-11-1-11-1−i−iii−i−iiiii−i−ii−i
χ151111111111111-1-1-1-11-1-1-1-1-1-11111111111-1-1-1-11-1-11ii−i−i−i−iii−i−iiii−i
χ161111111111111-1-1-1-11-1-1-1-1-1-11111111111-1-1-1-11-1-11−i−iiiii−i−iii−i−i−ii
χ1722222222222222-22-22222020-2-22200-2-20000-200-20000000000000000
χ1822222222222222-22-2222-20-20-2-2-2-200220000-20020000000000000000
χ192222222222222-22-222-2-22020-2-2-2-200220000200-20000000000000000
χ202222222222222-22-222-2-2-20-20-2-22200-2-2000020020000000000000000
χ2122222222222-2-222-22-2-220000-2200220000-2-2-22000-200000000000000
χ2222222222222-2-222-22-2-220000-2200-2-2000022-2-2000200000000000000
χ2322222222222-2-22-2-2-2-2-2202022-2000000-2-2002020-2000000000000000
χ2422222222222-2-22-2-2-2-2-220-20-22-2000000220020-202000000000000000
χ2522222222222-2-2-2222-22-202022-20000002200-20-20-2000000000000000
χ2622222222222-2-2-2222-22-20-20-22-2000000-2-200-20202000000000000000
χ2722222222222-2-2-2-22-2-22-20000-2200220000222-2000-200000000000000
χ2822222222222-2-2-2-22-2-22-20000-2200-2-20000-2-222000200000000000000
χ29444444-4-44-4-40000400-4000000000000000000000002-22-20000000000
χ30444444-4-44-4-40000400-400000000000000000000000-22-220000000000
χ31444444-4-44-4-40000-4004000000000000000000000002i−2i−2i2i0000000000
χ32444444-4-44-4-40000-400400000000000000000000000−2i2i2i−2i0000000000
χ3344444-444-4-4-400400000-40000000000000000000000000000002i−2i2i−2i00
χ3444444-444-4-4-400400000-4000000000000000000000000000000−2i2i−2i2i00
χ3544444-444-4-4-400-40000040000000000000000000000000000002-2-2200
χ3644444-444-4-4-400-4000004000000000000000000000000000000-222-200
χ3744444-4-4-4-444440000-4000000004-40000000000000000000000000000
χ3844444-4-4-4-444440000-400000000-440000000000000000000000000000
χ3944444-4-4-4-444-4-4000040000000000004-4000000000000000000000000
χ4044444-4-4-4-444-4-400004000000000000-44000000000000000000000000
χ41888-8-8800-800000000000000000000000004i−4i00000000000000000000
χ42888-8-8800-80000000000000000000000000−4i4i00000000000000000000
χ43888-8-8-800800000000000040-400000000000000000000000000000000
χ44888-8-8-8008000000000000-40400000000000000000000000000000000
χ4588-88-800008-800000000040-4000000000000000000000000000000000
χ4688-88-800008-8000000000-404000000000000000000000000000000000
χ4788-88-80000-888-80000000000000000000000000000000000000000000
χ4888-88-80000-88-880000000000000000000000000000000000000000000
χ4988-8-8808-80000000000000000000000004-40000000000000000000000
χ5088-8-8808-8000000000000000000000000-440000000000000000000000
χ5188-8-880-88000000000000000000004-400000000000000000000000000
χ5288-8-880-8800000000000000000000-4400000000000000000000000000
χ5316-1600000000000040-4000000000000000000000000000002i−2i2i−2i000000
χ5416-1600000000000040-400000000000000000000000000000−2i2i−2i2i000000
χ5516-16000000000000-404000000000000000000000000000002-2-22000000
χ5616-16000000000000-40400000000000000000000000000000-222-2000000

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