Finite Group Databasebeta

← Group #72337598

Character table — Group #72337598

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122244444488161616161616161616161616161616323232323232323232323232323232323232323232646464646464646464128128128128
order12222222222222222222222444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1-1ii−i−iii−i−iii−i−i
χ4111111111111111111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1-1−i−iii−i−iii−i−iii
χ51111111111111111111-1-1111-1-1111-1-1-1-11111-1-1-1-111-1-1-1-111-11111-1-1-1-11-11-1
χ61111111111111111111-1-1111-1-1111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-11111-11-11
χ71111111111111111111-1-1-1-11-1-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-11ii−i−i−i−iiii−i−ii
χ81111111111111111111-1-1-1-11-1-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-11−i−iiiii−i−i−iii−i
χ9111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111111-1-1-1-1
χ10111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-11111
χ11111111111111111-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-111-1-1-1-1-1ii−i−iii−i−i−i−iii
χ12111111111111111-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-111-1-1-1-1-1−i−iii−i−iiiii−i−i
χ13111111111111111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-11111-1-1-1-11111-11111-1-1-1-1-11-11
χ14111111111111111-1-1-1-1-1-1111-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-11-1
χ15111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-11ii−i−i−i−iii−iii−i
χ16111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-11−i−iiiii−i−ii−i−ii
χ172222222222222-2-20000222222222-200220000000000-2-200-2-2-2000000000000
χ182222222222222-2-2000022-2-2222-2-2-200-2-20000000000-2-200222000000000000
χ192222222222222-2-20000-2-2222-2-222-200-2-200000000002200-2-22000000000000
χ202222222222222-2-20000-2-2-2-22-2-2-2-2-200220000000000220022-2000000000000
χ2122222222222-2-2222222002-2-200-22-2000022-2-20000-2-200002-20000000000000
χ2222222222222-2-222222200-22-2002-2-20000-2-2220000-2-20000-220000000000000
χ2322222222222-2-222-2-2-2-2002-2-200-22-20000-2-22200002200002-20000000000000
χ2422222222222-2-222-2-2-2-200-22-2002-2-2000022-2-20000220000-220000000000000
χ2522222222222-2-2-2-20000002-2-200-2222200000022-2-20000-2-2-220000000000000
χ2622222222222-2-2-2-20000002-2-200-222-2-2000000-2-222000022-220000000000000
χ2722222222222-2-2-2-2000000-22-2002-2222000000-2-2220000-2-22-20000000000000
χ2822222222222-2-2-2-2000000-22-2002-22-2-200000022-2-20000222-20000000000000
χ29444444-4-44-4-4000000000004000-4000000000000000000000002-22-200000000
χ30444444-4-44-4-4000000000004000-400000000000000000000000-22-2200000000
χ31444444-4-44-4-400000000000-40004000000000000000000000002i−2i−2i2i00000000
χ32444444-4-44-4-400000000000-4000400000000000000000000000−2i2i2i−2i00000000
χ3344444-44-4-44-40000000000400000-4000000000000000000000000002i−2i2i−2i0000
χ3444444-44-4-44-40000000000400000-400000000000000000000000000−2i2i−2i2i0000
χ3544444-44-4-44-40000000000-4000004000000000000000000000000002-2-220000
χ3644444-44-4-44-40000000000-400000400000000000000000000000000-222-20000
χ3744444-4-44-4-44440000004-400-44-4000000000000000000000000000000000000
χ3844444-4-44-4-4444000000-4400-4-44000000000000000000000000000000000000
χ3944444-4-44-4-44-4-40000000000400000000000000000004-400000000000000000
χ4044444-4-44-4-44-4-4000000000040000000000000000000-4400000000000000000
χ4144-4-4400-40044-40022-2-2040000-40002-200000000002-2002-2000000000000000
χ4244-4-4400-40044-40022-2-20-400004000-2200000000002-200-22000000000000000
χ4344-4-4400-40044-400-2-222040000-4000-220000000000-2200-22000000000000000
χ4444-4-4400-40044-400-2-2220-4000040002-20000000000-22002-2000000000000000
χ4544-4-4400-4004-440022-2-240000-400002-20000000000-2200-22000000000000000
χ4644-4-4400-4004-440022-2-2-4000040000-220000000000-22002-2000000000000000
χ4744-4-4400-4004-4400-2-22240000-40000-2200000000002-2002-2000000000000000
χ4844-4-4400-4004-4400-2-222-40000400002-200000000002-200-22000000000000000
χ49888-8-80800-8000000000000000000000000000004i−4i000000000000000000000
χ50888-8-80800-800000000000000000000000000000−4i4i000000000000000000000
χ51888-8-80-8008000000000000000000000004-4000000000000000000000000000
χ52888-8-80-800800000000000000000000000-44000000000000000000000000000
χ5388-88-8800-800000000000000000000000000004i−4i00000000000000000000000
χ5488-88-8800-80000000000000000000000000000−4i4i00000000000000000000000
χ5588-88-8-8008000000000000000000000000004-40000000000000000000000000
χ5688-88-8-800800000000000000000000000000-440000000000000000000000000
χ5788-8-8800800-8000000000000000000004-400000000000000000000000000000
χ5888-8-8800800-800000000000000000000-4400000000000000000000000000000
χ5916-16000000000004-44-44-40000000000000000000000000000000000000000000
χ6016-16000000000004-4-44-440000000000000000000000000000000000000000000
χ6116-1600000000000-444-4-440000000000000000000000000000000000000000000
χ6216-1600000000000-44-444-40000000000000000000000000000000000000000000

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