Finite Group Databasebeta

← Group #72337564

Character table — Group #72337564

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size112224444448888888888888888881616161616161616161616161616163232323232323232323232323232323232646464646464646464128128128128
order12222222222222222222222224444222222444444444244444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111-1-1-1-111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111-1-1-1-11111111111-1-11111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111111-1-1-1-1
χ611111111111111111-1-1-1-11111111111-1-11111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-11111
χ711111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1iiii−i−i−i−i−i−iii
χ811111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1−i−i−i−iiiiiii−i−i
χ91111111111111-1-1-1-111111111-1-1-1-11111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-111-1-111-1-11-11-1
χ101111111111111-1-1-1-111111111-1-1-1-11111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-111-1-111-11-11
χ111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-11-1-1-1-11111-1-111-1-11ii−i−i−i−iiii−i−ii
χ121111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-11-1-1-1-11111-1-111-1-11−i−iiiii−i−i−iii−i
χ131111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111-1-11111111-1-1-1-11111-1-1-1-111-111-1-111-1-1-11-11
χ141111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111-1-11111111-1-1-1-11111-1-1-1-111-1-1-111-1-1111-11-1
χ151111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-11111111111111-1-1-1-1-1-1-1-1-1-11ii−i−i−i−iii−iii−i
χ161111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-11111111111111-1-1-1-1-1-1-1-1-1-11−i−iiiii−i−ii−i−ii
χ1722222222222222222000022222222-2-2002222222000000-200000000-2-200-2-2-2000000000000
χ18222222222222222220000-2-2-2-22222-2-200-2-22-2-2-2-2000000-200000000-2-200222000000000000
χ192222222222222-2-2-2-200002222-2-2-2-2-2-200-2-2222-2-2000000-2000000002200-2-22000000000000
χ202222222222222-2-2-2-20000-2-2-2-2-2-2-2-2-2-200222-2-222000000-200000000220022-2000000000000
χ2122222222222-2-20000000022-2-20000-2-20000-22-2002222-2-22000022-2-200002-20000000000000
χ2222222222222-2-20000000022-2-20000-2-20000-22-200-2-2-2-22220000-2-22200002-20000000000000
χ2322222222222-2-200000000-2-2220000-2-20000-2-22002222-2-220000-2-2220000-220000000000000
χ2422222222222-2-200000000-2-2220000-2-20000-2-2200-2-2-2-2222000022-2-20000-220000000000000
χ2522222222222-2-20000222222-2-20000222200-22-200000000-222-2-2000000-2-2-220000000000000
χ2622222222222-2-200002222-2-2220000222200-2-2200000000-2-2-222000000-2-22-20000000000000
χ2722222222222-2-20000-2-2-2-222-2-2000022-2-200-22-200000000-2-2-22200000022-220000000000000
χ2822222222222-2-20000-2-2-2-2-2-222000022-2-200-2-2200000000-222-2-2000000222-20000000000000
χ29444444-4-44-4-400000000000044000000000000-4000000000000000000000000002-2002-20000
χ30444444-4-44-4-400000000000044000000000000-400000000000000000000000000-2200-220000
χ31444444-4-44-4-4000000000000-4-40000000000004000000000000000000000000002i−2i00−2i2i0000
χ32444444-4-44-4-4000000000000-4-4000000000000400000000000000000000000000−2i2i002i−2i0000
χ3344444-44-4-44-40000000000440000000000000-400000000000000000000000002-2002-2000000
χ3444444-44-4-44-40000000000440000000000000-40000000000000000000000000-2200-22000000
χ3544444-44-4-44-40000000000-4-40000000000000400000000000000000000000002i−2i00−2i2i000000
χ3644444-44-4-44-40000000000-4-4000000000000040000000000000000000000000−2i2i002i−2i000000
χ3744444-4-44-4-444444-4-40000000044-4-4000000-400000000000000000000000000000000000000
χ3844444-4-44-4-4444-4-44400000000-4-444000000-400000000000000000000000000000000000000
χ3944444-4-44-4-44-4-40000000000000000000000400000000000000000004-400000000000000000
χ4044444-4-44-4-44-4-4000000000000000000000040000000000000000000-4400000000000000000
χ41444-4-400-40044-400442222000000-4-400-2-2000000022-2-22-2000000000002-2000000000000000
χ42444-4-400-40044-40044-2-2-2-2000000-4-400220000000-2-222-2200000000000-22000000000000000
χ43444-4-400-40044-400-4-422220000004400-2-20000000-2-222-22000000000002-2000000000000000
χ44444-4-400-40044-400-4-4-2-2-2-2000000440022000000022-2-22-200000000000-22000000000000000
χ45444-4-400-4004-44440022220000-4-40000-2-20000000-2-2222-200000000000-22000000000000000
χ46444-4-400-4004-444400-2-2-2-20000-4-4000022000000022-2-2-22000000000002-2000000000000000
χ47444-4-400-4004-44-4-40022220000440000-2-2000000022-2-2-2200000000000-22000000000000000
χ48444-4-400-4004-44-4-400-2-2-2-20000440000220000000-2-2222-2000000000002-2000000000000000
χ4944-44-40-40040002-22-222-2-24-4002-22-2002-22-20002-22-22-20002-2002-2000000000000000000000
χ5044-44-40-40040002-22-222-2-2-44002-22-2002-2-22000-222-22-2000-2200-22000000000000000000000
χ5144-44-40-40040002-22-2-2-2224-4002-22-200-222-20002-2-22-22000-2200-22000000000000000000000
χ5244-44-40-40040002-22-2-2-222-44002-22-200-22-22000-22-22-220002-2002-2000000000000000000000
χ5344-44-40-4004000-22-2222-2-24-400-22-22002-2-22000-22-22-220002-200-22000000000000000000000
χ5444-44-40-4004000-22-2222-2-2-4400-22-22002-22-20002-2-22-22000-22002-2000000000000000000000
χ5544-44-40-4004000-22-22-2-2224-400-22-2200-22-22000-222-22-2000-22002-2000000000000000000000
χ5644-44-40-4004000-22-22-2-222-4400-22-2200-222-20002-22-22-20002-200-22000000000000000000000
χ5744-4-44-400400002-2-2222-2-2004-4-222-200-222-2000-22-222-2000002-2002-20000000000000000000
χ5844-4-44-400400002-2-2222-2-200-44-222-200-22-220002-2-222-200000-2200-220000000000000000000
χ5944-4-44-400400002-2-22-2-222004-4-222-2002-22-2000-222-2-2200000-2200-220000000000000000000
χ6044-4-44-400400002-2-22-2-22200-44-222-2002-2-220002-22-2-22000002-2002-20000000000000000000
χ6144-4-44-40040000-222-222-2-2004-42-2-2200-22-220002-22-2-22000002-200-220000000000000000000
χ6244-4-44-40040000-222-222-2-200-442-2-2200-222-2000-222-2-2200000-22002-20000000000000000000
χ6344-4-44-40040000-222-2-2-222004-42-2-22002-2-220002-2-222-200000-22002-20000000000000000000
χ6444-4-44-40040000-222-2-2-22200-442-2-22002-22-2000-22-222-2000002-200-220000000000000000000
χ65888-8-800800-8000000000000000000000044000-4-40000000000000000000000000000000000
χ66888-8-800800-80000000000000000000000-4-4000440000000000000000000000000000000000
χ6788-88-80800-80004-4-44000000004-4-44000000000000000000000000000000000000000000000
χ6888-88-80800-8000-444-400000000-444-4000000000000000000000000000000000000000000000
χ6988-8-88800-800004-44-400000000-44-44000000000000000000000000000000000000000000000
χ7088-8-88800-80000-44-44000000004-44-4000000000000000000000000000000000000000000000
χ7116-16000000000000000008-8000000004-40000000000000000000000000000000000000000000
χ7216-1600000000000000000-88000000004-40000000000000000000000000000000000000000000
χ7316-160000000000000008-80000000000-440000000000000000000000000000000000000000000
χ7416-16000000000000000-880000000000-440000000000000000000000000000000000000000000

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