Finite Group Databasebeta

← Group #72221753

Character table — Group #72221753

Order 6400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118
size112224444444488888101010101010101016161616161616161616161616161616161616162020202020202020252540404040404040404040404040405050508080808080808080808080808080808080808080100100100100100100100100100100100100100100100100200200200200200200200200200
order1222255101010101010210101010222222225101010101010101010101010101010101010104444444422444444101010101010101022220202020202020202020202020202020202020204444444444444444244444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1111111-1-111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-111111111-1-111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111
χ511111111111111111111-1-111-1-1111111111111111111111111ii−i−i-1-11-111i−i11-1-111-1-1-1-1-111-1-111111111iiii−i−i−i−i-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1i−iii−i−i
χ611111111111111111111-1-111-1-1111111111111111111111111−i−iii-1-11-111−ii11-1-111-1-1-1-1-111-1-111111111−i−i−i−iiiii-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1−ii−i−iii
χ711111111111111111111-1-111-1-111111111111111111111-1-1-1-1ii−i−i-1-11-1-1-1i−i11-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111ii−i−i−i−i−i−iiiii-111i−i−i−iii
χ811111111111111111111-1-111-1-111111111111111111111-1-1-1-1−i−iii-1-11-1-1-1−ii11-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−iiiiiii−i−i−i−i-111−iiii−i−i
χ9111111111111111111-1-111-1-11111111111111111111111ii−i−i1111-1-1-11i−i11-1-111-1-111-1-1-1-1-111iiii−i−i−i−i11111111ii−i−i-1-1-1-1ii−i−iii−i−i-1i−i-1-1i−ii−i
χ10111111111111111111-1-111-1-11111111111111111111111ii−i−i-1-1-1-1-1-1-11i−i-1-1-1-111-1-111-1-1-1-1-111iiii−i−i−i−i-1-1-1-1-1-1-1-1ii−i−i1111−i−iii−i−iii-1i−i11−ii−ii
χ11111111111111111111-1-111-1-11111111111111111111111−i−iii1111-1-1-11−ii11-1-111-1-111-1-1-1-1-111−i−i−i−iiiii11111111−i−iii-1-1-1-1−i−iii−i−iii-1−ii-1-1−ii−ii
χ12111111111111111111-1-111-1-11111111111111111111111−i−iii-1-1-1-1-1-1-11−ii-1-1-1-111-1-111-1-1-1-1-111−i−i−i−iiiii-1-1-1-1-1-1-1-1−i−iii1111ii−i−iii−i−i-1−ii11i−ii−i
χ13111111111111111111-1-1-1-1-1-1-1-111111111111111111111ii−i−iii−i−i11-1-1i−ii−i-1-1-1-1-1-1-1-1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-11111-1-11−ii−ii-111-1
χ14111111111111111111-1-1-1-1-1-1-1-111111111111111111111ii−i−i−i−iii11-1-1i−i−ii-1-1-1-1-1-1-1-1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-1111−iii−i1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-111111111111111111111−i−iiiii−i−i11-1-1−iii−i-1-1-1-1-1-1-1-1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii11-1-1-1-1111i−i−ii1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-111111111111111111111−i−iii−i−iii11-1-1−ii−ii-1-1-1-1-1-1-1-1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-11111-1-11i−ii−i-111-1
χ171111111111111-11111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111111-1-1-1-111-1-111-1-111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1
χ181111111111111-11111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111111-1-1-1-111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ191111111111111-11111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111111111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111
χ201111111111111-11111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111-11111-1-1-1-1
χ211111111111111-1111111-1-111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111ii−i−i-1-1-11-1-1−ii11-1-111-1-1-1-1-1-1-11111-1-111-1-1ii−i−i−i−iii-1-1-1-1ii−i−iiiii−i−i−i−i111−ii−i−iii
χ221111111111111-1111111-1-111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111−i−iii-1-1-11-1-1i−i11-1-111-1-1-1-1-1-1-11111-1-111-1-1−i−iiiii−i−i-1-1-1-1−i−iii−i−i−i−iiiii111i−iii−i−i
χ231111111111111-1111111-1-111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1111−ii11-1-111-1-1-1-1-1-1-111-1-111-1-111ii−i−i−i−iii1111ii−i−i−i−i−i−iiiii1-1-1−iiii−i−i
χ241111111111111-1111111-1-111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1111i−i11-1-111-1-1-1-1-1-1-111-1-111-1-111−i−iiiii−i−i1111−i−iiiiiii−i−i−i−i1-1-1i−i−i−iii
χ251111111111111-11111-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1ii−i−i1111-1-11-1−ii-1-1-1-111-1-111-1-1-111-1-1ii−i−i−i−iii11-1-111-1-1ii−i−i-1-1-1-1ii−i−iii−i−i1−ii11−ii−ii
χ261111111111111-11111-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-11-1−ii11-1-111-1-111-1-1-111-1-1ii−i−i−i−iii-1-111-1-111ii−i−i1111−i−iii−i−iii1−ii-1-1i−ii−i
χ271111111111111-11111-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1−i−iii1111-1-11-1i−i-1-1-1-111-1-111-1-1-111-1-1−i−iiiii−i−i11-1-111-1-1−i−iii-1-1-1-1−i−iii−i−iii1i−i11i−ii−i
χ281111111111111-11111-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-11-1i−i11-1-111-1-111-1-1-111-1-1−i−iiiii−i−i-1-111-1-111−i−iii1111ii−i−iii−i−i1i−i-1-1−ii−ii
χ291111111111111-11111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1ii−i−iii−i−i1111−ii−ii-1-1-1-1-1-1-1-11111111ii−i−i−i−iiiii−i−i−i−iii−i−iii−i−iii-1-11111-1-1-1i−ii−i1-1-11
χ301111111111111-11111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1ii−i−i−i−iii1111−iii−i-1-1-1-1-1-1-1-11111111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111-1i−i−ii-111-1
χ311111111111111-11111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1−i−iiiii−i−i1111i−i−ii-1-1-1-1-1-1-1-11111111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111-1−iii−i-111-1
χ321111111111111-11111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1−i−iii−i−iii1111i−ii−i-1-1-1-1-1-1-1-11111111−i−iiiii−i−i−i−iiiii−i−iii−i−iii−i−i-1-11111-1-1-1−ii−ii1-1-11
χ33222-2-22222-2-22202-2-2-2222-2-2-22-220000222-2-2-2-2000000002i−2i2i−2i0000-2-2000000222-2-2-22-22-2200002i−2i002i−2i00000000002i−2i2i−2i000000000000000000000
χ34222-2-22222-2-22202-2-2-2222-2-2-22-220000222-2-2-2-200000000−2i2i−2i2i0000-2-2000000222-2-2-22-22-220000−2i2i00−2i2i0000000000−2i2i−2i2i000000000000000000000
χ35222-2-22222-2-22202-2-2-222-22-2-2-2220000222-2-2-2-2000000002i−2i2i−2i00002200000022-22-2-2-22-22-200002i−2i002i−2i0000000000−2i2i−2i2i000000000000000000000
χ36222-2-22222-2-22202-2-2-222-22-2-2-2220000222-2-2-2-200000000−2i2i−2i2i00002200000022-22-2-2-22-22-20000−2i2i00−2i2i00000000002i−2i2i−2i000000000000000000000
χ37222-2-22222-2-22202-2-2-2-2-22-2222-220000222-2-2-2-2000000002-2-22000022000000-2-22-2222-2-22-200002-200-2200000000002-2-22000000000000000000000
χ38222-2-22222-2-22202-2-2-2-2-22-2222-220000222-2-2-2-200000000-222-2000022000000-2-22-2222-2-22-20000-22002-20000000000-222-2000000000000000000000
χ39222-2-22222-2-22202-2-2-2-2-2-2222-2220000222-2-2-2-2000000002-2-220000-2-2000000-2-2-2222-222-2200002-200-220000000000-222-2000000000000000000000
χ40222-2-22222-2-22202-2-2-2-2-2-2222-2220000222-2-2-2-200000000-222-20000-2-2000000-2-2-2222-222-220000-22002-200000000002-2-22000000000000000000000
χ4122-22-222-2-222220-22-2-22-2222-2-2-2200002-2-222-2-20000000000002i−2i2i−2i-2-20000002-2222-2-2-2-2220000000000002i−2i002i−2i0000002i−2i2i−2i00000000000000000
χ4222-22-222-2-222220-22-2-22-2222-2-2-2200002-2-222-2-2000000000000−2i2i−2i2i-2-20000002-2222-2-2-2-222000000000000−2i2i00−2i2i000000−2i2i−2i2i00000000000000000
χ4322-22-222-2-222220-22-2-22-2-2-22-222200002-2-222-2-20000000000002-2-22220000002-2-2-22-2222-2-20000000000002-200-220000002-2-2200000000000000000
χ4422-22-222-2-222220-22-2-22-2-2-22-222200002-2-222-2-2000000000000-222-2220000002-2-2-22-2222-2-2000000000000-22002-2000000-222-200000000000000000
χ4522-22-222-2-222220-22-2-2-2222-22-2-2200002-2-222-2-20000000000002i−2i2i−2i22000000-2222-22-2-22-2-20000000000002i−2i002i−2i000000−2i2i−2i2i00000000000000000
χ4622-22-222-2-222220-22-2-2-2222-22-2-2200002-2-222-2-2000000000000−2i2i−2i2i22000000-2222-22-2-22-2-2000000000000−2i2i00−2i2i0000002i−2i2i−2i00000000000000000
χ4722-22-222-2-222220-22-2-2-22-2-2-2222200002-2-222-2-20000000000002-2-22-2-2000000-22-2-2-2222-2220000000000002-200-22000000-222-200000000000000000
χ4822-22-222-2-222220-22-2-2-22-2-2-2222200002-2-222-2-2000000000000-222-2-2-2000000-22-2-2-2222-222000000000000-22002-20000002-2-2200000000000000000
χ4922-2-2222-2-2-2-2220-2-2222-22-2-22-22200002-2-2-2-2220000000000000000220000002-22-2-22-22-2-2200000000000000000000000000002-22-22-22-2000000000
χ5022-2-2222-2-2-2-2220-2-2222-22-2-22-22200002-2-2-2-2220000000000000000220000002-22-2-22-22-2-220000000000000000000000000000-22-22-22-22000000000
χ5122-2-2222-2-2-2-2220-2-2222-2-22-222-2200002-2-2-2-2220000000000000000-2-20000002-2-22-222-222-200000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000
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χ58444444-144-1-14-14-144-144004400-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-400000040-4-400-1-100-1-100000-1-10011111111000000000000000000000000000000000
χ59444444-144-1-14-14-144-1-4-400-4-400-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14i4i−4i−4i000000-404i−4i00110011000001100−i−i−i−iiiii000000000000000000000000000000000
χ60444444-144-1-14-14-144-1-4-400-4-400-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−4i−4i4i4i000000-40−4i4i00110011000001100iiii−i−i−i−i000000000000000000000000000000000
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χ7044444-14-1-144-14-44-1-1400440044-111-4-4-1-1-1-1-1-1-1111111110000-4-4-4-4000-4004400-1-100-1-100000110000000011-1-111-1-10000000000000000000000000
χ7144444-14-1-144-14-44-1-1400-4-400-4-4-111-4-4-1-1-1-1-1-1-11111111100004i4i−4i−4i000400−4i4i0011001100000-1-100000000−i−iiiii−i−i0000000000000000000000000
χ7244444-14-1-144-14-44-1-1400-4-400-4-4-111-4-4-1-1-1-1-1-1-1111111110000−4i−4i4i4i0004004i−4i0011001100000-1-100000000ii−i−i−i−iii0000000000000000000000000
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χ77444-4-44-144114-10-1-4-41-4-4004400-1005−5-1-1-111115555−5−5−5−54-4-440000000000001100-1-100000−5500-115−51-1−55000000000000000000000000000000000
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χ79444-4-44-144114-10-1-4-41-4-4004400-100−55-1-1-11111−5−5−5−555554-4-440000000000001100-1-1000005−500-11−551-15−5000000000000000000000000000000000
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χ8244-44-4-141144-140-4-11-4004400-4-4-15−500-111-1-11155−5−555−5−50000−4i4i−4i4i0000000000-1-10011000005−500000000i−i−i5i5i−i−i5i50000000000000000000000000
χ8344-44-4-141144-140-4-11-4004400-4-4-1−5500-111-1-111−5−555−5−55500004i−4i4i−4i0000000000-1-1001100000−5500000000−ii−i5i5−ii−i5i50000000000000000000000000
χ8444-44-4-141144-140-4-11-4004400-4-4-1−5500-111-1-111−5−555−5−5550000−4i4i−4i4i0000000000-1-1001100000−5500000000i−ii5−i5i−ii5−i50000000000000000000000000
χ8544-44-4-141144-140-4-11-400-4-40044-15−500-111-1-11155−5−555−5−500004-4-4400000000001100-1-100000−5500000000-115−51-1−550000000000000000000000000
χ8644-44-4-141144-140-4-11-400-4-40044-15−500-111-1-11155−5−555−5−50000-444-400000000001100-1-100000−55000000001-1−55-115−50000000000000000000000000
χ8744-44-4-141144-140-4-11-400-4-40044-1−5500-111-1-111−5−555−5−55500004-4-4400000000001100-1-1000005−500000000-11−551-15−50000000000000000000000000
χ8844-44-4-141144-140-4-11-400-4-40044-1−5500-111-1-111−5−555−5−5550000-444-400000000001100-1-1000005−5000000001-15−5-11−550000000000000000000000000
χ89888-8-8-28-2-2-8-8-280822-8008-8008-8-20000-2-2-2222200000000000000000000000000-2200-22000000000000000000000000000000000000000000000000
χ90888-8-8-28-2-2-8-8-280822-800-8800-88-20000-2-2-22222000000000000000000000000002-2002-2000000000000000000000000000000000000000000000000
χ9188-88-88-2-8-8-2-28-2028-828-8008-800-20000-222-2-222000000000000000000000000-2200-2200000000000000000000000000000000000000000000000000
χ9288-88-88-2-8-8-2-28-2028-82-8800-8800-20000-222-2-2220000000000000000000000002-2002-200000000000000000000000000000000000000000000000000
χ9388-8-888-2-8-8228-202-88-28-800-8800-20000-22222-2-2000000000000000000000000-22002-200000000000000000000000000000000000000000000000000
χ9488-8-888-2-8-8228-202-88-2-88008-800-20000-22222-2-20000000000000000000000002-200-2200000000000000000000000000000000000000000000000000
χ9588-8-88-2822-8-8-280-82-28008-800-88-20000-22222-2-200000000000000000000000000-22002-2000000000000000000000000000000000000000000000000
χ9688-8-88-2822-8-8-280-82-2800-88008-8-20000-22222-2-2000000000000000000000000002-200-22000000000000000000000000000000000000000000000000
χ978-8000880000-8-8000000000000080000-800000000000000000000008-800000000000000000000000000000000000000000000000000000000000000
χ988-8000880000-8-8000000000000080000-80000000000000000000000-8800000000000000000000000000000000000000000000000000000000000000
χ991616161616-4-4-4-4-4-4-4-416-4-4-4-4000000001-4-4-4-4111111111111111000000000000000000000000000000000000000000000000000000000000000000000000
χ1001616161616-4-4-4-4-4-4-4-4-16-4-4-4-400000000144441111111-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000000000000000000000
χ101161616-16-16-4-4-4-444-4-40-44440000000010045−45111-1-1-1-1−5−5−5−55555000000000000000000000000000000000000000000000000000000000000000000000000
χ102161616-16-16-4-4-4-444-4-40-444400000000100−4545111-1-1-1-15555−5−5−5−5000000000000000000000000000000000000000000000000000000000000000000000000
χ1031616-1616-16-4-444-4-4-4-404-44400000000145−45001-1-111-1-1−5−555−5−555000000000000000000000000000000000000000000000000000000000000000000000000
χ1041616-1616-16-4-444-4-4-4-404-444000000001−4545001-1-111-1-155−5−555−5−5000000000000000000000000000000000000000000000000000000000000000000000000
χ1051616-16-1616-4-44444-4-4044-4-400000000100001-1-1-1-11155-5-5-5-555000000000000000000000000000000000000000000000000000000000000000000000000
χ1061616-16-1616-4-44444-4-4044-4-400000000100001-1-1-1-111-5-55555-5-5000000000000000000000000000000000000000000000000000000000000000000000000
χ10716-1600016-40045−45-1640000000000000-4000040045−450000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10816-1600016-400−4545-1640000000000000-40000400−45450000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10916-16000-41645−45004-160000000000000-40000445−45000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11016-16000-416−4545004-160000000000000-400004−4545000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11116-16000-4-445−4545−4544000000000000010000-1−55−555-55−55−25−5+255+25−5−255−5000000000000000000000000000000000000000000000000000000000000000000000000
χ11216-16000-4-445−4545−4544000000000000010000-1−55−555-5−55−5+255−25−5−255+25−55000000000000000000000000000000000000000000000000000000000000000000000000
χ11316-16000-4-445−45−454544000000000000010000-1−555−5-555+25−5−255−5−55−5+255−25000000000000000000000000000000000000000000000000000000000000000000000000
χ11416-16000-4-445−45−454544000000000000010000-1−555−5-55−5−255+25−555−55−25−5+25000000000000000000000000000000000000000000000000000000000000000000000000
χ11516-16000-4-4−454545−4544000000000000010000-15−5−55-555−25−5+25−555−5−5−255+25000000000000000000000000000000000000000000000000000000000000000000000000
χ11616-16000-4-4−454545−4544000000000000010000-15−5−55-55−5+255−255−5−555+25−5−25000000000000000000000000000000000000000000000000000000000000000000000000
χ11716-16000-4-4−4545−454544000000000000010000-15−55−55-55−5−5−255+25−5+255−255−5000000000000000000000000000000000000000000000000000000000000000000000000
χ11816-16000-4-4−4545−454544000000000000010000-15−55−55-5−555+25−5−255−25−5+25−55000000000000000000000000000000000000000000000000000000000000000000000000

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