Finite Group Databasebeta

← Group #72221722

Character table — Group #72221722

Order 6400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size11222444488888881010101010101010161616161616161620202020202020202020202025253232323232324040404040404040404040405050508080808080808080808080808080808080808080100100100100100100100100100100100100100100100100200200200200200200200200200
order1222255101041010101010104444444451010102020202088888888202020202210102020202044888820202020202022220202020404040404040404040404040404040404444444488888888444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111111111111111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-111-1-1
χ311111111111111111111111111111111-1-1-1-1111111111111111111-1-1111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1
χ5111111111111111111-1-111-1-1111111111111ii−i−i11-1-1-1-11111111-111i−i11-1-11-1-1-1-111-1-11111ii−i−i1111ii−i−iii−i−iii−i−i-1-1-1-1ii−i−i-1ii−i−i-1-1i−i
χ6111111111111111111-1-111-1-1111111111111−i−iii11-1-1-1-11111111-111−ii11-1-11-1-1-1-111-1-11111−i−iii1111−i−iii−i−iii−i−iii-1-1-1-1−i−iii-1−i−iii-1-1−ii
χ7111111111111111111-1-111-1-111111111-1-1-1-1ii−i−i11-1-1-1-11111111-1-1-1i−i11-1-11-1-1-1-111-1-1-1-1-1-1ii−i−i-1-1-1-1ii−i−i−i−iii−i−iii1111ii−i−i-1−i−iii11i−i
χ8111111111111111111-1-111-1-111111111-1-1-1-1−i−iii11-1-1-1-11111111-1-1-1−ii11-1-11-1-1-1-111-1-1-1-1-1-1−i−iii-1-1-1-1−i−iiiii−i−iii−i−i1111−i−iii-1ii−i−i11−ii
χ91111111111111111-1-111-1-11111111111ii−i−i1111-1-111-1-1111111-11i−i11-1-111-11-1-1-1-1-111ii−i−i1111ii−i−i1111i−ii−ii−ii−iii−i−i-1-1-1-1-1i−ii−ii−i-1-1
χ101111111111111111-1-111-1-11111111111ii−i−i-1-1-1-1-1-111-1-1111111-11i−i-1-1-1-111-11-1-1-1-1-111ii−i−i-1-1-1-1ii−i−i-1-1-1-1−ii−ii−ii−iiii−i−i1111-1−ii−iii−i11
χ111111111111111111-1-111-1-11111111111−i−iii1111-1-111-1-1111111-11−ii11-1-111-11-1-1-1-1-111−i−iii1111−i−iii1111−ii−ii−ii−ii−i−iii-1-1-1-1-1−ii−ii−ii-1-1
χ121111111111111111-1-111-1-11111111111−i−iii-1-1-1-1-1-111-1-1111111-11−ii-1-1-1-111-11-1-1-1-1-111−i−iii-1-1-1-1−i−iii-1-1-1-1i−ii−ii−ii−i−i−iii1111-1i−ii−i−ii11
χ131111111111111111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i-1-1-1-111111111-1-1i−ii−i-1-1-1-1-1-1111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-111-1-111-1−i−iii−i−iii1-111-1−ii−ii
χ141111111111111111-1-1-1-1-1-1-1-111111111ii−i−i−i−iii-1-1-1-111111111-1-1i−i−ii-1-1-1-1-1-1111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11−i−iiiii−i−i11-1-11−iii−i
χ151111111111111111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i-1-1-1-111111111-1-1−iii−i-1-1-1-1-1-1111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11ii−i−i−i−iii11-1-11i−i−ii
χ161111111111111111-1-1-1-1-1-1-1-111111111−i−iii−i−iii-1-1-1-111111111-1-1−ii−ii-1-1-1-1-1-1111-1-1-1-1−i−iii−i−iii−i−iii−i−iii-111-1-111-1ii−i−iii−i−i1-111-1i−ii−i
χ17111111111-1111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1
χ18111111111-1111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-111
χ19111111111-1111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1111111-1-1
χ20111111111-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ21111111111-111111111-1-111-1-11111-1-1-1-11111ii−i−i11-1-1-1-111-1-1-1-1-11-1-1−ii11-1-11-1-1-1-1-1-111-1-1-1-1−i−iii1111ii−i−iii−i−iii−i−i-1-1-1-1ii−i−i1−i−iii11−ii
χ22111111111-111111111-1-111-1-11111-1-1-1-11111−i−iii11-1-1-1-111-1-1-1-1-11-1-1i−i11-1-11-1-1-1-1-1-111-1-1-1-1ii−i−i1111−i−iii−i−iii−i−iii-1-1-1-1−i−iii1ii−i−i11i−i
χ23111111111-111111111-1-111-1-11111-1-1-1-1-1-1-1-1ii−i−i11-1-1-1-111-1-1-1-1-1111−ii11-1-11-1-1-1-1-1-1111111−i−iii-1-1-1-1ii−i−i−i−iii−i−iii1111ii−i−i1ii−i−i-1-1−ii
χ24111111111-111111111-1-111-1-11111-1-1-1-1-1-1-1-1−i−iii11-1-1-1-111-1-1-1-1-1111i−i11-1-11-1-1-1-1-1-1111111ii−i−i-1-1-1-1−i−iiiii−i−iii−i−i1111−i−iii1−i−iii-1-1i−i
χ25111111111-1111111-1-111-1-1111111-1-1-1-1ii−i−i1111-1-111-1-111-1-1-1-11-1−ii-1-1-1-111-11-1-1-111-1-1−i−iii-1-1-1-1ii−i−i1111i−ii−ii−ii−iii−i−i-1-1-1-11−ii−ii−ii11
χ26111111111-1111111-1-111-1-1111111-1-1-1-1ii−i−i-1-1-1-1-1-111-1-111-1-1-1-11-1−ii11-1-111-11-1-1-111-1-1−i−iii1111ii−i−i-1-1-1-1−ii−ii−ii−iiii−i−i11111i−ii−i−ii-1-1
χ27111111111-1111111-1-111-1-1111111-1-1-1-1−i−iii1111-1-111-1-111-1-1-1-11-1i−i-1-1-1-111-11-1-1-111-1-1ii−i−i-1-1-1-1−i−iii1111−ii−ii−ii−ii−i−iii-1-1-1-11i−ii−ii−i11
χ28111111111-1111111-1-111-1-1111111-1-1-1-1−i−iii-1-1-1-1-1-111-1-111-1-1-1-11-1i−i11-1-111-11-1-1-111-1-1ii−i−i1111−i−iii-1-1-1-1i−ii−ii−ii−i−i−iii11111−ii−iii−i-1-1
χ29111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-111−ii−ii-1-1-1-1-1-11111111−i−iii−i−iiiii−i−iii−i−i-111-1-111-1−i−iii−i−iii-11-1-11i−ii−i
χ30111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i−i−iii-1-1-1-11111-1-1-1-111−iii−i-1-1-1-1-1-11111111−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11−i−iiiii−i−i-1-111-1i−i−ii
χ31111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iiiii−i−i-1-1-1-11111-1-1-1-111i−i−ii-1-1-1-1-1-11111111ii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11ii−i−i−i−iii-1-111-1−iii−i
χ32111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-111i−ii−i-1-1-1-1-1-11111111ii−i−iii−i−i−i−iii−i−iii-111-1-111-1ii−i−iii−i−i-11-1-11−ii−ii
χ33222-2-22222022-2-2-2-2222-2-2-22-222-2-2000000002-22-2-2-2-2-2-2-22-20000000000222-2-2222-200000000000000002-22-20000000000002-22-2000000000
χ34222-2-22222022-2-2-2-2222-2-2-22-222-2-200000000-22-22-2-2-2-2-2-22-20000000000222-2-2222-20000000000000000-22-22000000000000-22-22000000000
χ35222-2-22222022-2-2-2-222-22-2-2-2222-2-2000000002i−2i−2i2i-2-222222-2000000000022-22-2-2-2-2200000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000000
χ36222-2-22222022-2-2-2-222-22-2-2-2222-2-200000000−2i2i2i−2i-2-222222-2000000000022-22-2-2-2-220000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000000
χ37222-2-22222022-2-2-2-2-2-22-2222-222-2-2000000002-22-222-2-2222-20000000000-2-22-222-2-2200000000000000002-22-2000000000000-22-22000000000
χ38222-2-22222022-2-2-2-2-2-22-2222-222-2-200000000-22-2222-2-2222-20000000000-2-22-222-2-220000000000000000-22-220000000000002-22-2000000000
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χ4122-22-222220-2-222-2-22-2222-2-2-222-2-200002-22-20000-2-2-2-2-2-2-2200000000002-2222-22-220000000000002-22-20000000000002-22-20000000000000
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χ4322-22-222220-2-222-2-22-2-2-22-22222-2-200002-22-20000-2-22222-2200000000002-2-2-222-22-20000000000002-22-2000000000000-22-220000000000000
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χ8544-44-4-14-1401-4-141-4-4400-4400-1-111i5−i5004i−4i−4i4i0000-1-100001-1i5−i5i5−i50000001-10010000−i5i500−555−50000−iii−i00000000000000000000000000000
χ8644-44-4-14-1401-4-141-4-4400-4400-1-111i5−i500−4i4i4i−4i0000-1-100001-1i5−i5i5−i50000001-10010000−i5i5005−5−550000i−i−ii00000000000000000000000000000
χ8744-44-4-14-1401-4-141-4-4400-4400-1-111−i5i5004i−4i−4i4i0000-1-100001-1−i5i5−i5i50000001-10010000i5−i5005−5−550000−iii−i00000000000000000000000000000
χ8844-44-4-14-1401-4-141-4-4400-4400-1-111−i5i500−4i4i4i−4i0000-1-100001-1−i5i5−i5i50000001-10010000i5−i500−555−50000i−i−ii00000000000000000000000000000
χ89888-8-8-28-280-282-82-88800-8-800-2-222000000000000220000-220000000000-2-20020000000000000000000000000000000000000000000000000
χ90888-8-8-28-280-282-82-8-8-8008800-2-222000000000000-2-20000-2200000000002200-20000000000000000000000000000000000000000000000000
χ9188-88-88-28-20-828-2-82008800-8-8-2-2220000000000000022002-2000000000000-2-202000000000000000000000000000000000000000000000000
χ9288-88-88-28-20-828-2-8200-8-80088-2-22200000000000000-2-2002-2000000000000220-2000000000000000000000000000000000000000000000000
χ9388-8-888-28-20-82-828-2008-800-88-2-2-2-200000000000000-2-20022000000000000-2202000000000000000000000000000000000000000000000000
χ9488-8-888-28-20-82-828-200-88008-8-2-2-2-2000000000000002200220000000000002-20-2000000000000000000000000000000000000000000000000
χ9588-8-88-28-2802-82-8-288-800-8800-2-2-2-2000000000000-2-20000220000000000-220020000000000000000000000000000000000000000000000000
χ9688-8-88-28-2802-82-8-28-88008-800-2-2-2-20000000000002200002200000000002-200-20000000000000000000000000000000000000000000000000
χ978-800088-8-80000000000000008-80000000000000000008-8000000000000000000000000000000000000000000000000000000000000000000
χ988-800088-8-80000000000000008-8000000000000000000-88000000000000000000000000000000000000000000000000000000000000000000
χ991616161616-4-4-4-416-4-4-4-4-4-4000000001111-4-4-4-400000000000000111111000000000000000000000000000000000000000000000000000000000000
χ1001616161616-4-4-4-4-16-4-4-4-4-4-400000000111144440000000000000011-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ101161616-16-16-4-4-4-40-4-444440000000011-1-1004i5−4i5000000000000001-1−i5−i5i5i5000000000000000000000000000000000000000000000000000000000000
χ102161616-16-16-4-4-4-40-4-444440000000011-1-100−4i54i5000000000000001-1i5i5−i5−i5000000000000000000000000000000000000000000000000000000000000
χ1031616-1616-16-4-4-4-4044-4-4440000000011-1-14i5−4i50000000000000000-11−i5i5−i5i5000000000000000000000000000000000000000000000000000000000000
χ1041616-1616-16-4-4-4-4044-4-4440000000011-1-1−4i54i50000000000000000-11i5−i5i5−i5000000000000000000000000000000000000000000000000000000000000
χ1051616-16-1616-4-4-4-404444-4-4000000001111000000000000000000-1-15-5-55000000000000000000000000000000000000000000000000000000000000
χ1061616-16-1616-4-4-4-404444-4-4000000001111000000000000000000-1-1-555-5000000000000000000000000000000000000000000000000000000000000
χ10716-1600016-4-164000000000000000-4400000000000000004i5−4i500000000000000000000000000000000000000000000000000000000000000000000
χ10816-1600016-4-164000000000000000-440000000000000000−4i54i500000000000000000000000000000000000000000000000000000000000000000000
χ10916-16000-4164-16000000000000000-44000000000000004i5−4i50000000000000000000000000000000000000000000000000000000000000000000000
χ11016-16000-4164-16000000000000000-4400000000000000−4i54i50000000000000000000000000000000000000000000000000000000000000000000000
χ11132-32000-8-8880000000000000002-210-10000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11232-32000-8-8880000000000000002-2-1010000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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