Finite Group Databasebeta

← Group #72311107

Character table — Group #72311107

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97
size1122244444444888888888881616161616161616161616161616161632323232323232323232323232326464646464646464646464646464646464646464646464646464646464646464646464128128128128128128128128
order1222222222222222222222222222222244444444224444444444444444444444444444444444444444444444444888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ511111111111111111-1-111111111-1-1-111111-1-1-1-111-11-111111-1-1-1-11-11111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111-1-111111111-1-1-111111-1-1-1-111-11-111111-1-1-1-11-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-111111111-1-1-111111-1-1-1-111-11-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111-1-111111111-1-1-111111-1-1-1-111-11-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ9111111111111111-1-1111-1-1-1-11-1-11-1-11-11-1-111-1-11111-111-1-1-11-1-1-1-1111111-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i
χ10111111111111111-1-1111-1-1-1-11-1-11-1-11-11-1-111-1-11111-111-1-1-11-1-1-1-1111111-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii
χ11111111111111111-1-1111-1-1-1-11-1-11-1-11-11-1-111-1-11111-111-1-1-11-1-1-1-11-1-1-1-11-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii
χ12111111111111111-1-1111-1-1-1-11-1-11-1-11-11-1-111-1-11111-111-1-1-11-1-1-1-11-1-1-1-11-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i
χ13111111111111111-1-1-1-11-1-1-1-11-1-1-1111-11-1-1-1-11111-11111-1-1-1-1111-1-11111-11-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii
χ14111111111111111-1-1-1-11-1-1-1-11-1-1-1111-11-1-1-1-11111-11111-1-1-1-1111-1-11111-11-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i
χ15111111111111111-1-1-1-11-1-1-1-11-1-1-1111-11-1-1-1-11111-11111-1-1-1-1111-1-1-1-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−i
χ16111111111111111-1-1-1-11-1-1-1-11-1-1-1111-11-1-1-1-11111-11111-1-1-1-1111-1-1-1-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii
χ171111111-1-11-1-111-11111-1111111-1111-1-11-1-11111-11-1-1-11-111-1-1-111-1-1ii−i−i1-1ii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ181111111-1-11-1-111-11111-1111111-1111-1-11-1-11111-11-1-1-11-111-1-1-111-1-1ii−i−i1-1ii−i−i-1-111-1-111-1-111-1-111−i−iii−i−iiii−ii−i−ii−ii
χ191111111-1-11-1-111-11111-1111111-1111-1-11-1-11111-11-1-1-11-111-1-1-111-1-1−i−iii1-1−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii−ii−ii−ii−ii
χ201111111-1-11-1-111-11111-1111111-1111-1-11-1-11111-11-1-1-11-111-1-1-111-1-1−i−iii1-1−i−iii-1-111-1-111-1-111-1-111ii−i−iii−i−i−ii−iii−ii−i
χ211111111-1-11-1-111-111-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1-111-111-111-111-1-1-11ii−i−i-11ii−i−i11-1-111-1-1-1-111-1-111ii−i−iii−i−i−ii−ii−ii−ii
χ221111111-1-11-1-111-111-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1-111-111-111-111-1-1-11ii−i−i-11ii−i−i-1-111-1-11111-1-111-1-1−i−iii−i−iii−ii−iii−ii−i
χ231111111-1-11-1-111-111-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1-111-111-111-111-1-1-11−i−iii-11−i−iii11-1-111-1-1-1-111-1-111−i−iii−i−iiii−ii−ii−ii−i
χ241111111-1-11-1-111-111-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1-111-111-111-111-1-1-11−i−iii-11−i−iii-1-111-1-11111-1-111-1-1ii−i−iii−i−ii−ii−i−ii−ii
χ251111111-1-11-1-111-1-1-111-1-1-1-1-11-111-1-1-1111111-1-1-11-1-111-1-1-11-11-1-11-1ii−i−i11−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1i−i−ii-111-1
χ261111111-1-11-1-111-1-1-111-1-1-1-1-11-111-1-1-1111111-1-1-11-1-111-1-1-11-11-1-11-1ii−i−i11−i−iii−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111i−i−ii1-1-11
χ271111111-1-11-1-111-1-1-111-1-1-1-1-11-111-1-1-1111111-1-1-11-1-111-1-1-11-11-1-11-1−i−iii11ii−i−iii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111−iii−i1-1-11
χ281111111-1-11-1-111-1-1-111-1-1-1-1-11-111-1-1-1111111-1-1-11-1-111-1-1-11-11-1-11-1−i−iii11ii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−iii−i-111-1
χ291111111-1-11-1-111-1-1-1-1-1-1-1-1-1-11-11-111-11111-1-111-111-1-11-1-1-111-11111ii−i−i-1-1−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1−iii−i1-1-11
χ301111111-1-11-1-111-1-1-1-1-1-1-1-1-1-11-11-111-11111-1-111-111-1-11-1-1-111-11111ii−i−i-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−iii−i-111-1
χ311111111-1-11-1-111-1-1-1-1-1-1-1-1-1-11-11-111-11111-1-111-111-1-11-1-1-111-11111−i−iii-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111i−i−ii-111-1
χ321111111-1-11-1-111-1-1-1-1-1-1-1-1-1-11-11-111-11111-1-111-111-1-11-1-1-111-11111−i−iii-1-1ii−i−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1i−i−ii1-1-11
χ33222222222222222220022222-222000-22-2220000-22020-2-2-2-2-20000-2000000000002-22-22-22-2000000000000000000000000
χ34222222222222222220022222-222000-22-2220000-22020-2-2-2-2-20000-200000000000-22-22-22-22000000000000000000000000
χ3522222222222222222002-2-2-2-2-222000-22-2-2-20000-2-20-2022-2220000-200000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ3622222222222222222002-2-2-2-2-222000-22-2-2-20000-2-20-2022-2220000-20000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ3722222222222222222222-2-2-2-22222-2-2222-2-222-2-22-22-2-2-2-22-2-22-2222-20000-22000000000000000000000000000000000000
χ3822222222222222222-2-22-2-2-2-2222-222222-2-2-2-2222-2-2-22-2-22-2-2-22-2-22200002-2000000000000000000000000000000000000
χ39222222222222222-2-20022222-2-2-2000-2-2-2220000-2-20-20222-2-20000200000000000000000002-22-2-22-220000000000000000
χ40222222222222222-2-20022222-2-2-2000-2-2-2220000-2-20-20222-2-2000020000000000000000000-22-222-22-20000000000000000
χ41222222222222222-2-2002-2-2-2-2-2-2-2000-2-2-2-2-20000-22020-2-222200002000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ42222222222222222-2-2002-2-2-2-2-2-2-2000-2-2-2-2-20000-22020-2-22220000200000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ43222222222222222-2-222222222-2-22222-222222222-22-22-2-2-22222-2-2-2-20000-2-2000000000000000000000000000000000000
χ44222222222222222-2-2-2-2222222-2-2-2-2-22-2222-2-2-2-22-2-2-2-2-2-2-222-2-222-22000022000000000000000000000000000000000000
χ452222222-2-22-2-222-22200-22222-22-20002-2-2-2-20000220-20-22-2-2200002000000000002-2-222-2-22000000000000000000000000
χ462222222-2-22-2-222-22200-22222-22-20002-2-2-2-20000220-20-22-2-220000200000000000-222-2-222-2000000000000000000000000
χ472222222-2-22-2-222-22200-2-2-2-2-2-22-20002-2-22200002-20202-2-22-20000200000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ482222222-2-22-2-222-22200-2-2-2-2-2-22-20002-2-22200002-20202-2-22-2000020000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ492222222-2-22-2-222-22222-2-2-2-2-222-22-2-2-2-222222-2-2-2-2-222-222-22-2222-220000-2-2000000000000000000000000000000000000
χ502222222-2-22-2-222-222-2-2-2-2-2-2-222-2-222-2-2222-2-222-2-222-2-222-222-2-2-2-2-2000022000000000000000000000000000000000000
χ512222222-2-22-2-222-2-2-200-22222-2-2200022-2-2-200002-20202-22-220000-200000000000000000002-2-22-222-20000000000000000
χ522222222-2-22-2-222-2-2-200-22222-2-2200022-2-2-200002-20202-22-220000-20000000000000000000-222-22-2-220000000000000000
χ532222222-2-22-2-222-2-2-200-2-2-2-2-2-2-2200022-2220000220-20-2222-20000-2000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ542222222-2-22-2-222-2-2-200-2-2-2-2-2-2-2200022-2220000220-20-2222-20000-200000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ552222222-2-22-2-222-2-2-222-222222-22222-222-2-22222-2-2-22-2-22-22-2-2-2-2-2220000-22000000000000000000000000000000000000
χ562222222-2-22-2-222-2-2-2-2-2-222222-22-2-2-2-222-2-2-2-2-2-2-2-2222-22-22-222222-200002-2000000000000000000000000000000000000
χ57444444444-4-4-4-4-440000-444-4-40000000004-4000000000000000000002i−2i2i−2i002i−2i2i−2i00000000000000000000000000000000
χ58444444444-4-4-4-4-440000-444-4-40000000004-400000000000000000000−2i2i−2i2i00−2i2i−2i2i00000000000000000000000000000000
χ59444444444-4-4-4-4-440000-4-4-444000000000-44000000000000000000002i−2i2i−2i00−2i2i−2i2i00000000000000000000000000000000
χ60444444444-4-4-4-4-440000-4-4-444000000000-4400000000000000000000−2i2i−2i2i002i−2i2i−2i00000000000000000000000000000000
χ614444444-4-4-444-4-4-40000444-4-4000000000-44000000000000000000002-2-22002-2-2200000000000000000000000000000000
χ624444444-4-4-444-4-4-40000444-4-4000000000-4400000000000000000000-222-200-222-200000000000000000000000000000000
χ634444444-4-4-444-4-4-400004-4-4440000000004-4000000000000000000002-2-2200-222-200000000000000000000000000000000
χ644444444-4-4-444-4-4-400004-4-4440000000004-400000000000000000000-222-2002-2-2200000000000000000000000000000000
χ6544444-4-4444444-4-40000-40000-400044-4040000-4-440004000000-40000000000000000000000000000000000000000000000
χ6644444-4-4444444-4-40000-40000-4000-4-4-4040000444000-400000040000000000000000000000000000000000000000000000
χ6744444-4-4444444-4-40044-4000040040040-400-4-400-4040000000-400000000000000000000000000000000000000000000000
χ6844444-4-4444444-4-400-4-4-40000400-40040-4004400-40-40000000400000000000000000000000000000000000000000000000
χ6944444-4-4-4-44-4-44-44000040000-4000444040000-4-4-4000-400000040000000000000000000000000000000000000000000000
χ7044444-4-4-4-44-4-44-44000040000-4000-4-4404000044-40004000000-40000000000000000000000000000000000000000000000
χ7144444-4-4-4-44-4-44-44004440000400400-40-400-4-40040-40000000400000000000000000000000000000000000000000000000
χ7244444-4-4-4-44-4-44-4400-4-440000400-400-40-40044004040000000-400000000000000000000000000000000000000000000000
χ7388888-8-888-8-8-8-88-80000800000000000000000000000000000000000000000000000000000000000000000000000000000
χ7488888-8-8-8-8-888-8880000-800000000000000000000000000000000000000000000000000000000000000000000000000000
χ75888-8-8000008-80004400000000-440000-400000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ76888-8-8000008-80004400000000-440000-40000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ77888-8-8000008-8000-4-4000000004-40000400000000000000000000000000000000000000000000000002-22-2-22-2200000000
χ78888-8-8000008-8000-4-4000000004-4000040000000000000000000000000000000000000000000000000-22-222-22-200000000
χ79888-8-800000-880004400000000-4-40000400000000000000000000000000000000000000000000000002-2-222-2-2200000000
χ80888-8-800000-880004400000000-4-4000040000000000000000000000000000000000000000000000000-222-2-222-200000000
χ81888-8-800000-88000-4-400000000440000-400000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ82888-8-800000-88000-4-400000000440000-40000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ8388-8-888-80000000000440008-8000-44-4000004-44-40000000000000000000000000000000000000000000000000000000000
χ8488-8-888-8000000000044000-88000-4-44000004-4-440000000000000000000000000000000000000000000000000000000000
χ8588-8-888-80000000000-4-40008-80004-4400000-44-440000000000000000000000000000000000000000000000000000000000
χ8688-8-888-80000000000-4-4000-8800044-400000-444-40000000000000000000000000000000000000000000000000000000000
χ8788-8-88-8800000000004408-800000-44-400000-44-440000000000000000000000000000000000000000000000000000000000
χ8888-8-88-880000000000440-8800000-4-4400000-444-40000000000000000000000000000000000000000000000000000000000
χ8988-8-88-880000000000-4-408-8000004-44000004-44-40000000000000000000000000000000000000000000000000000000000
χ9088-8-88-880000000000-4-40-880000044-4000004-4-440000000000000000000000000000000000000000000000000000000000
χ911616-1616-160016-160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ921616-1616-1600-16160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9316-160000000-8008008-88-8000000000000000000000000000000004-400000000000000000000000000000000000000000000
χ9416-160000000-8008008-8-8800000000000000000000000000000000-4400000000000000000000000000000000000000000000
χ9516-160000000-800800-888-800000000000000000000000000000000-4400000000000000000000000000000000000000000000
χ9616-160000000-800800-88-88000000000000000000000000000000004-400000000000000000000000000000000000000000000
χ9732-3200000001600-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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