Finite Group Databasebeta

← Group #72324320

Character table — Group #72324320

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size112224444888881616161616161616161616161616161616163232323232323232326464646464646464646464646464128128128128
order12222222222222222222222444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-11111111-1-11-1-1-1-1-1-1-1-11-111-1-1ii−i−iii−i−iii−i−i
χ4111111111111111111111-1-11111111-1-11-1-1-1-1-1-1-1-11-111-1-1−i−iii−i−iii−i−iii
χ511111111111111111111-11-1111111-11-1-11-1-1-1-1-1-1-1-11-1-111i−ii−ii−ii−ii−ii−i
χ611111111111111111111-11-1111111-11-1-11-1-1-1-1-1-1-1-11-1-111−ii−ii−ii−ii−ii−ii
χ711111111111111111111-1-11111111-1-11-1-11111111-1-1-1-1-1-11-1-111-1-111-1-11
χ811111111111111111111-1-11111111-1-11-1-11111111-1-1-1-1-1-1-111-1-111-1-111-1
χ91111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ101111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-11-1-111-1-1-1-11-1-11-1-11111-1-11-1-1-111ii−i−iii−i−i−i−iii
χ121111111111111111-1-1-1-11-1-111-1-1-1-11-1-11-1-11111-1-11-1-1-111−i−iii−i−iiiii−i−i
χ131111111111111111-1-1-1-1-11-111-1-1-1-1-11-1-11-11111-1-1-1111-1-1i−ii−ii−ii−i−ii−ii
χ141111111111111111-1-1-1-1-11-111-1-1-1-1-11-1-11-11111-1-1-1111-1-1−ii−ii−ii−iii−ii−i
χ151111111111111111-1-1-1-1-1-1111-1-1-1-1-1-11-1-11-1-1-1-111-1-111111-1-111-1-11-111-1
χ161111111111111111-1-1-1-1-1-1111-1-1-1-1-1-11-1-11-1-1-1-111-1-11111-111-1-111-11-1-11
χ1722222222222222-2-20000222-2-200002222220000-2-2-2-20000000000000000
χ1822222222222222-2-200002-2-2-2-200002-2-22-2-2000022-220000000000000000
χ1922222222222222-2-20000-22-2-2-20000-22-2-22-20000222-20000000000000000
χ2022222222222222-2-20000-2-22-2-20000-2-22-2-220000-2-2220000000000000000
χ212222222222-2-2-2-2220000002-2-2000000200-200002-200000002200-2-200000
χ222222222222-2-2-2-2220000002-2-2000000200-200002-20000000-2-2002200000
χ232222222222-2-2-2-222000000-2-2-2000000-20020000-2200000002i−2i00−2i2i00000
χ242222222222-2-2-2-222000000-2-2-2000000-20020000-220000000−2i2i002i−2i00000
χ252222222222-2-2-2-2-2-2000000222000000200-20000-220000002002-200-20000
χ262222222222-2-2-2-2-2-2000000222000000200-20000-22000000-200-220020000
χ272222222222-2-2-2-2-2-2000000-222000000-200200002-20000002i00−2i−2i002i0000
χ282222222222-2-2-2-2-2-2000000-222000000-200200002-2000000−2i002i2i00−2i0000
χ29444444-4-44-4000000222200400-2-2-2-200-400022-2-200000000000000000000
χ30444444-4-44-4000000222200-400-2-2-2-2004000-2-22200000000000000000000
χ31444444-4-44-4000000-2-2-2-200400222200-4000-2-22200000000000000000000
χ32444444-4-44-4000000-2-2-2-200-400222200400022-2-200000000000000000000
χ3344444-444-4-44-44-40000000400000000400-40000000000000000000000000
χ3444444-444-4-44-44-40000000-400000000-40040000000000000000000000000
χ3544444-444-4-4-44-44000000400000000400-400000000000000000000000000
χ3644444-444-4-4-44-44000000-400000000-400400000000000000000000000000
χ3744-4-4404-4000-4040022-2-24000022-2-2-400000000000002-200000000000000
χ3844-4-4404-4000-4040022-2-2-4000022-2-240000000000000-2200000000000000
χ3944-4-4404-4000-40400-2-22240000-2-222-40000000000000-2200000000000000
χ4044-4-4404-4000-40400-2-222-40000-2-222400000000000002-200000000000000
χ4144-4-440-4400-40400022-2-204000-2-2220-4000000000000002-2000000000000
χ4244-4-440-4400-40400022-2-20-4000-2-2220400000000000000-22000000000000
χ4344-4-440-4400-404000-2-2220400022-2-20-400000000000000-22000000000000
χ4444-4-440-4400-404000-2-2220-400022-2-204000000000000002-2000000000000
χ4588888-8-8-8-880000000000000000000000000000000000000000000000000
χ46888-8-80000000000000000004-44-44-4000000000000000000000000000000
χ47888-8-80000000000000000004-4-44-44000000000000000000000000000000
χ48888-8-8000000000004-44-4000-440000000000000000000000000000000000
χ49888-8-800000000000-44-44000-440000000000000000000000000000000000
χ5088-88-80000000004-40000000004-4-44000000000000000000000000000000
χ5188-88-80000000004-4000000000-444-4000000000000000000000000000000
χ5288-88-8000000000-444-4-44000000000000000000000000000000000000000
χ5388-88-8000000000-44-444-4000000000000000000000000000000000000000
χ5488-8-8808-800080-8000000000000000000000000000000000000000000000
χ5588-8-880-880080-80000000000000000000000000000000000000000000000
χ5616-16000800-800000000000000000000000000004i−4i00000000000000000000
χ5716-16000800-80000000000000000000000000000−4i4i00000000000000000000
χ5816-16000-8008000000000000000000000000004-40000000000000000000000
χ5916-16000-800800000000000000000000000000-440000000000000000000000

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