Finite Group Databasebeta

← Group #72216719

Character table — Group #72216719

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11222444444448888888161616161616161616161616323232323232323232323264646464646464646464646464646464646464646464
order12222222222222222222222224444444224444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-11-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-11-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-11-1-11111111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-11-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ71111111111111111111111-1-11-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ81111111111111111111111-1-11-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-11-1-11-11111-1-1-111-11-1-1-1111-111-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ101111111111111111-1-1-1-1-1-11-1-11-11111-1-1-111-11-1-1-1111-111-1-1−i−iii−i−iii−ii−ii−ii−ii
χ111111111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-11111-11-111-1-11-1-1-111ii−i−iii−i−i−ii−ii−ii−ii
χ121111111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-11111-11-111-1-11-1-1-111−i−iii−i−iiii−ii−ii−ii−i
χ131111111111111111-1-1-1-1-1-1-11-1-111111-1-1-111-1-11-1-111-11-1-111ii−i−i−i−iiii−i−iii−i−ii
χ141111111111111111-1-1-1-1-1-1-11-1-111111-1-1-111-1-11-1-111-11-1-111−i−iiiii−i−i−iii−i−iii−i
χ151111111111111111-1-1-1-1-1-1-11-1-11-1-1-1-1-11111-1-1111-1-1-1111-1-1ii−i−i−i−iii−iii−i−iii−i
χ161111111111111111-1-1-1-1-1-1-11-1-11-1-1-1-1-11111-1-1111-1-1-1111-1-1−i−iiiii−i−ii−i−iii−i−ii
χ1722222222222222222222222-2-22-20000-200-2-2-22-20000-2200000000000000000000
χ182222222222222222222222-22-2-220000-200-2-2-2-2200002-200000000000000000000
χ192222222222222222-2-2-2-2-2-2222220000200-2-22220000-2-200000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-22-2-20000200-2-22-2-200002200000000000000000000
χ2122222222-2-2-2-222-2-222-2-22-20020000002002-2-2000000000000000000002200-2-200
χ2222222222-2-2-2-222-2-222-2-22-20020000002002-2-200000000000000000000-2-2002200
χ2322222222-2-2-2-222-2-222-2-22-200-2000000-200-22200000000000000000000002i−2i00−2i2i
χ2422222222-2-2-2-222-2-222-2-22-200-2000000-200-2220000000000000000000000−2i2i002i−2i
χ2522222222-2-2-2-222-2-2-2-222-22002000000200-22-200000000000000000000002200-2-2
χ2622222222-2-2-2-222-2-2-2-222-22002000000200-22-20000000000000000000000-2-20022
χ2722222222-2-2-2-222-2-2-2-222-2200-2000000-2002-22000000000000000000002i−2i00−2i2i00
χ2822222222-2-2-2-222-2-2-2-222-2200-2000000-2002-2200000000000000000000−2i2i002i−2i00
χ29444444-4-400004-400000000004002222-42200000-2-2-2-20000000000000000000000
χ30444444-4-400004-40000000000400-2-2-2-2-4-2-20000022220000000000000000000000
χ31444444-4-400004-40000000000-40022224-2-20000022-2-20000000000000000000000
χ32444444-4-400004-40000000000-400-2-2-2-242200000-2-2220000000000000000000000
χ3344444-44444-4-4-4-44-40000000400400000000000-400000000000000000000000000
χ3444444-44444-4-4-4-44-40000000-400-400000000000400000000000000000000000000
χ3544444-444-4-444-4-4-44000000400400000000000-4000000000000000000000000000
χ3644444-444-4-444-4-4-44000000-400-4000000000004000000000000000000000000000
χ3744-4-4404-40044000-4000000400-4022-2-200000000002-2002-2000000000000000000
χ3844-4-4404-40044000-4000000400-40-2-2220000000000-2200-22000000000000000000
χ3944-4-4404-40044000-4000000-4004022-2-200000000002-200-22000000000000000000
χ4044-4-4404-40044000-4000000-40040-2-2220000000000-22002-2000000000000000000
χ4144-4-440-44440000-400000000400-422-2-20000000000-2200002-20000000000000000
χ4244-4-440-44440000-400000000400-4-2-22200000000002-20000-220000000000000000
χ4344-4-440-44440000-400000000-400422-2-20000000000-220000-220000000000000000
χ4444-4-440-44440000-400000000-4004-2-22200000000002-200002-20000000000000000
χ4588888-8-8-80000-88000000000000000000000000000000000000000000000000000
χ46888-8-80000000000000440-400000000000000000000000000000002-22-200000000
χ47888-8-80000000000000440-40000000000000000000000000000000-22-2200000000
χ48888-8-80000000000000-4-40400000000000000000000000000000002i−2i−2i2i00000000
χ49888-8-80000000000000-4-4040000000000000000000000000000000−2i2i2i−2i00000000
χ5088-88-8000000000004400-400000000000000000000000000002-22-2000000000000
χ5188-88-8000000000004400-40000000000000000000000000000-22-22000000000000
χ5288-88-800000000000-4-400400000000000000000000000000002i−2i−2i2i000000000000
χ5388-88-800000000000-4-40040000000000000000000000000000−2i2i2i−2i000000000000
χ5488-8-8808-800-8-800080000000000000000000000000000000000000000000000000
χ5588-8-880-88-8-80000800000000000000000000000000000000000000000000000000
χ568-8000-4004-44-440004-44-40000000004-402-2000002-2000000000000000000000000
χ578-8000-4004-44-440004-44-4000000000-440-2200000-22000000000000000000000000
χ588-8000-4004-44-44000-44-440000000004-40-2200000-22000000000000000000000000
χ598-8000-4004-44-44000-44-44000000000-4402-2000002-2000000000000000000000000
χ608-8000-400-44-4440004-4-4400000004-40002-200000-22000000000000000000000000
χ618-8000-400-44-4440004-4-440000000-44000-22000002-2000000000000000000000000
χ628-8000-400-44-444000-444-400000004-4000-22000002-2000000000000000000000000
χ638-8000-400-44-444000-444-40000000-440002-200000-22000000000000000000000000
χ6416-160008008-8-88-80000000000000000000000000000000000000000000000000000
χ6516-16000800-888-8-80000000000000000000000000000000000000000000000000000

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