Finite Group Databasebeta

← Group #72321647

Character table — Group #72321647

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97
size112224444444488888881616161616161616161616161616161616163232323232323232323232323232323232323232323232323232646464646464646464646464646464646464646464128128128128128128128128128128128128
order1222222222222222224422222444444444444422222444444444444444444444444444444444444444444448888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1111111111-1-111111111111-11-11-11-1111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1111-1-11111-1-11111-1-1111111-1111-11-11-1-11-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11-1-11111-1-1-1-111-1-1111111-1-11-1-1-1-1-1-1-11-1-1-1-1-11-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1111111-11111-111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-111-1-111-111-11-11-111-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1111111-1-1-111-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-1-111-1-1-1-11-11-1-1-1111111-1-111
χ7111111111111111111111111111111-1-1-1-111111-11111-1111-1-1-1-111-1-111-1-1-1-1-1-1-11111111-11-1-1-1111-1-11-11-1-111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-111111-11-1-11-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11-11-1-11-1-1-11-1-1-1-11-1111-1-1111111-1-1
χ91111111111111111-1-1111-1-1-111111111111111-11-111-11-1-1-11111-1-1111111-1-1-1-111-11-11-1-1-11-11-1-1-1-1-1-11-11111111-1-1-1-1-1-1
χ101111111111111111-1-1111-1-1-111111111111111-11-1-1-1-11-1-1-1111111111111-1-1-1-11-1-1-1-1-1-11-11-11-1-111-1-11-11-1-1-1-1-1-1111111
χ111111111111111111-1-1111-1-1-111111111111111-1-1111-1-11-1-111-1-1-1-111-1-111-1-1-1-1-11-11111-11-1-1-111-1-1-11-11-1-1-1-1-111-1-11111
χ121111111111111111-1-1111-1-1-111111111111111-1-11-1-1-1-11-1-111-1-11111-1-111-1-1-1-1-1-1-1-11-1111-1-1-11111-11-11-11111-1-111-1-1-1-1
χ131111111111111111-1-1111-1-1-1111111-1-1-1-11111-11111-111-1-1-1-111-1-1-1-1-1-1-1-1111111-11111-1-1-111-11-1-11-1-1-1-111-1-1-1-111-1-111
χ141111111111111111-1-1111-1-1-1111111-1-1-1-11111-111-1-1-111-1-1-1-11111-1-1-1-1-1-111111-1-1-11-111-1-111-11111-1-1-1-1-1-11111-1-111-1-1
χ151111111111111111-1-1111-1-1-1111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-11-11-1-1111-11-1-1-111111-1-111-1-11111-1-1
χ161111111111111111-1-1111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-11111-11-1111111111-1-111-1-1-1-111
χ1722222222222222222222-2222-2-2-2-2220000-2-2-22-20200-20222000000002200000000-2020-200-2000-2000020-2000000000000
χ1822222222222222222222-2222-2-2-2-2220000-2-2-22-20-200-20-22200000000-2-200000000-20-20200200020000-202000000000000
χ19222222222222222222-2-2222222-2-2-2-200002-2-2-2-22000-220-2-200-2-200000000000020200000-200-22000020-20000000000000
χ20222222222222222222-2-2222222-2-2-2-200002-2-2-2-2-2000-2-20-2-20022000000000000-202000002002-20000-2020000000000000
χ21222222222222222222-2-2-2222-2-222-2-22222-222-220000200-2-2-2-20000-2-20022222200-20000000-200000-20000000000000000
χ22222222222222222222-2-2-2222-2-222-2-2-2-2-2-2-222-220000200-2-22200002200-2-2-2-2-2-200-2000000020000020000000000000000
χ232222222222222222-2-222-2-2-2-2-2-2-2-2220000-2-2-2220200202-2-200000000-2-2000000002020-2002000-20000-202000000000000
χ242222222222222222-2-222-2-2-2-2-2-2-2-2220000-2-2-2220-20020-2-2-200000000220000000020-20200-20002000020-2000000000000
χ252222222222222222-2-2-2-22-2-2-222-2-2-2-200002-2-2-2220002202200-2-200000000000020-200000200-2-20000-2020000000000000
χ262222222222222222-2-2-2-22-2-2-222-2-2-2-200002-2-2-22-20002-20220022000000000000-20-200000-20022000020-20000000000000
χ272222222222222222-2-2-2-2-2-2-2-2-2-222-2-22222-222-2-20000-20022-2-20000-2-20022-2-2-2-2002000000020000020000000000000000
χ282222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-222-2-20000-200222200002200-2-222220020000000-200000-20000000000000000
χ292222222-222-2-2-22-2-20022-2000-22222-22i2i−2i−2i2-2-2-200000000002i−2i00222i−2i002i−2i000000000002000000-2-2000000000002i−2i0000
χ302222222-222-2-2-22-2-20022-2000-22222-22i2i−2i−2i2-2-2-200000000002i−2i00-2-22i−2i002i−2i00000000000-20000002200000000000−2i2i0000
χ312222222-222-2-2-22-2-20022-2000-22222-2−2i−2i2i2i2-2-2-20000000000−2i2i0022−2i2i00−2i2i000000000002000000-2-200000000000−2i2i0000
χ322222222-222-2-2-22-2-20022-2000-22222-2−2i−2i2i2i2-2-2-20000000000−2i2i00-2-2−2i2i00−2i2i00000000000-200000022000000000002i−2i0000
χ332222222-222-2-2-22-2-200-2-220002-222-222i2i−2i−2i-2-2-220002200000−2i2i0000−2i2i002i−2i0000020-20-200000000000000000002i−2i000000
χ342222222-222-2-2-22-2-200-2-220002-222-222i2i−2i−2i-2-2-22000-2-200000−2i2i0000−2i2i002i−2i00000-202020000000000000000000−2i2i000000
χ352222222-222-2-2-22-2-200-2-220002-222-22−2i−2i2i2i-2-2-2200022000002i−2i00002i−2i00−2i2i0000020-20-20000000000000000000−2i2i000000
χ362222222-222-2-2-22-2-200-2-220002-222-22−2i−2i2i2i-2-2-22000-2-2000002i−2i00002i−2i00−2i2i00000-2020200000000000000000002i−2i000000
χ37222222-222-2222-2-2-200222000-2-22-2-22000022-2-2000000000000000000220022-2-20000000022202000-2-2-2-2-2000000000000
χ38222222-222-2222-2-2-200222000-2-22-2-22000022-2-20000000000000000002200-2-22200000000-22-20-200022-22-2000000000000
χ39222222-222-2222-2-2-200222000-2-22-2-22000022-2-2000000000000000000-2-20022-2-200000000-2-220-2000-22222000000000000
χ40222222-222-2222-2-2-200222000-2-22-2-22000022-2-2000000000000000000-2-200-2-222000000002-2-2020002-22-22000000000000
χ41222222-222-2222-2-2-20022-200022-22-222222-2-22-20200002000-2-222002222-2-20000-200000000-20-2000000-202000000000000
χ42222222-222-2222-2-2-20022-200022-22-222222-2-22-20-20000-2000-2-2-2-20022-2-2-2-2000020000000020200000020-2000000000000
χ43222222-222-2222-2-2-20022-200022-22-22-2-2-2-2-2-22-20200002000222200-2-2-2-2220000-20000000020-200000020-2000000000000
χ44222222-222-2222-2-2-20022-200022-22-22-2-2-2-2-2-22-20-20000-200022-2-200-2-222220000200000000-202000000-202000000000000
χ45222222-222-2222-2-2-200-2-22000-2-2-222-222222-2220020000200220000-2-200-2-200000000-2020-20002-2000-2020000000000000
χ46222222-222-2222-2-2-200-2-22000-2-2-222-222222-22200-20000-200220000-2-200-2-20000000020-202000-2200020-20000000000000
χ47222222-222-2222-2-2-200-2-22000-2-2-222-2-2-2-2-22-2220020000200-2-2000022002200000000-20202000-2-200020-20000000000000
χ48222222-222-2222-2-2-200-2-22000-2-2-222-2-2-2-2-22-22200-20000-200-2-200002200220000000020-20-200022000-2020000000000000
χ49222222-222-2222-2-2-200-2-2-2000222-22-20000-22-22022000220000-2-20000000022-2-2-2000-20-2000-22020020000000000000000
χ50222222-222-2222-2-2-200-2-2-2000222-22-20000-22-2202-20002-20000-2-200000000-2-222-2000202000220-200-20000000000000000
χ51222222-222-2222-2-2-200-2-2-2000222-22-20000-22-220-22000-2200002200000000-2-2222000-20-20002-20200-20000000000000000
χ52222222-222-2222-2-2-200-2-2-2000222-22-20000-22-220-2-2000-2-20000220000000022-2-22000202000-2-20-20020000000000000000
χ53222222-2-22-2-2-2-2-22200222000-22-22-2-22i2i−2i−2i-22-220000000000−2i2i00002i−2i00−2i2i0000000000000000000000000000000002i−2i2-2
χ54222222-2-22-2-2-2-2-22200222000-22-22-2-22i2i−2i−2i-22-220000000000−2i2i00002i−2i00−2i2i000000000000000000000000000000000−2i2i-22
χ55222222-2-22-2-2-2-2-22200222000-22-22-2-2−2i−2i2i2i-22-2200000000002i−2i0000−2i2i002i−2i0000000000000000000000000000000002i−2i-22
χ56222222-2-22-2-2-2-2-22200222000-22-22-2-2−2i−2i2i2i-22-2200000000002i−2i0000−2i2i002i−2i000000000000000000000000000000000−2i2i2-2
χ57222222-2-22-2-2-2-2-22200-2-2-20002-2-22222i2i−2i−2i22-2-200000000002i−2i0000−2i2i00−2i2i00000000000000000000000002-22i−2i00000000
χ58222222-2-22-2-2-2-2-22200-2-2-20002-2-22222i2i−2i−2i22-2-200000000002i−2i0000−2i2i00−2i2i0000000000000000000000000-22−2i2i00000000
χ59222222-2-22-2-2-2-2-22200-2-2-20002-2-2222−2i−2i2i2i22-2-20000000000−2i2i00002i−2i002i−2i00000000000000000000000002-2−2i2i00000000
χ60222222-2-22-2-2-2-2-22200-2-2-20002-2-2222−2i−2i2i2i22-2-20000000000−2i2i00002i−2i002i−2i0000000000000000000000000-222i−2i00000000
χ614444444-444-4-4-44-4-4004440004-4-4-44-40000-444-400000000000000000000000000000000000000000000000000000000000
χ624444444-444-4-4-44-4-400-4-4-4000-44-4-4-440000444400000000000000000000000000000000000000000000000000000000000
χ63444444-4-44-4-4-4-4-4440044-40004-44-4-4-400004-44400000000000000000000000000000000000000000000000000000000000
χ64444444-4-44-4-4-4-4-44400-4-44000-444-4440000-4-44-400000000000000000000000000000000000000000000000000000000000
χ6544444-444-44-4-44-44-4000000000000000000000040022-4000000002200000000000-2020-20-20000002-200000000000000000
χ6644444-444-44-4-44-44-40000000000000000000000400-2-2-400000000-2-20000000000020-20202000000-2200000000000000000
χ6744444-444-44-4-44-44-40000000000000000000000-40022400000000-2-200000000000-2020-202000000-2200000000000000000
χ6844444-444-44-4-44-44-40000000000000000000000-400-2-2400000000220000000000020-2020-20000002-200000000000000000
χ6944444-44-4-4444-4-4-44440004-4-400000000000000000220000000002200000000000-20-2020-2000000-2200000000000000000
χ7044444-44-4-4444-4-4-44440004-4-400000000000000000-2-2000000000-2-2000000000002020-2020000002-200000000000000000
χ7144444-44-4-4444-4-4-44-4-4000-4440000000000000000022000000000-2-200000000000-20-202020000002-200000000000000000
χ7244444-44-4-4444-4-4-44-4-4000-44400000000000000000-2-200000000022000000000002020-20-2000000-2200000000000000000
χ7388888-8-88-8-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ7488888-8-8-8-8-888-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ75888-8-8800-80000000008i−8i000000000000000000040000-4000004i−4i000000000000000000000000000000000000000000000
χ76888-8-8800-80000000008i−8i0000000000000000000-40000400000−4i4i000000000000000000000000000000000000000000000
χ77888-8-8800-8000000000−8i8i000000000000000000040000-400000−4i4i000000000000000000000000000000000000000000000
χ78888-8-8800-8000000000−8i8i0000000000000000000-400004000004i−4i000000000000000000000000000000000000000000000
χ7988-88-80080000-800044000-44-40000004i−4i4i−4i00000000000000000000000000004i−4i000000000000000000000000000000000
χ8088-88-80080000-800044000-44-4000000−4i4i−4i4i0000000000000000000000000000−4i4i000000000000000000000000000000000
χ8188-88-80080000-8000-4-40004-440000004i−4i4i−4i0000000000000000000000000000−4i4i000000000000000000000000000000000
χ8288-88-80080000-8000-4-40004-44000000−4i4i−4i4i00000000000000000000000000004i−4i000000000000000000000000000000000
χ8388-88-800-80000800044000-4-440000004-4-44000000000000000000000000004-400000000000000000000000000000000000
χ8488-88-800-80000800044000-4-44000000-444-400000000000000000000000000-4400000000000000000000000000000000000
χ8588-88-800-800008000-4-400044-40000004-4-4400000000000000000000000000-4400000000000000000000000000000000000
χ8688-88-800-800008000-4-400044-4000000-444-4000000000000000000000000004-400000000000000000000000000000000000
χ8788-8-8800000-88000000000000000000000000000040000-44-4000000004-4000000000000000000000000000000000000000
χ8888-8-8800000-88000000000000000000000000000040000-4-4400000000-44000000000000000000000000000000000000000
χ8988-8-8800000-880000000000000000000000000000-4000044-400000000-44000000000000000000000000000000000000000
χ9088-8-8800000-880000000000000000000000000000-400004-44000000004-4000000000000000000000000000000000000000
χ91161616-16-16-1600160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ921616-16-16160000016-160000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9316-160000-80080000008-8000000000000000000000004-40000000004-40000000000000000000000000000000000000000000
χ9416-160000-80080000008-800000000000000000000000-44000000000-440000000000000000000000000000000000000000000
χ9516-160000-8008000000-88000000000000000000000004-4000000000-440000000000000000000000000000000000000000000
χ9616-160000-8008000000-8800000000000000000000000-440000000004-40000000000000000000000000000000000000000000
χ9732-3200001600-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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