Finite Group Databasebeta

← Group #72221619

Character table — Group #72221619

Order 6400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size11222444488888881010101010101010161616161616161620202020202020202020202025253232323232324040404040404040404040405050508080808080808080808080808080808080808080100100100100100100100100100100100100100100100100200200200200200200200200200
order1224455101021010202020202222444451010101010101088888888101010102210101010202022444410102020202024410101010202020202020202040404040404040404444444488888888244444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111111111111111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1111111111111111111-1-1111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11111
χ511111111111111111-11-11-11-1111111111111ii−i−i11-1-1-1-11111111-111i−i1-11-11-1-1-1-111-1-11111ii−i−i1111ii−i−iiiii−i−i−i−i-1-1-1-1ii−i−i-1-1-1i−iii−i−i
χ611111111111111111-11-11-11-1111111111111−i−iii11-1-1-1-11111111-111−ii1-11-11-1-1-1-111-1-11111−i−iii1111−i−iii−i−i−i−iiiii-1-1-1-1−i−iii-1-1-1−ii−i−iii
χ711111111111111111-11-11-11-111111111-1-1-1-1ii−i−i11-1-1-1-11111111-1-1-1i−i1-11-11-1-1-1-111-1-1-1-1-1-1ii−i−i-1-1-1-1ii−i−i−i−i−i−iiiii1111ii−i−i-111i−i−i−iii
χ811111111111111111-11-11-11-111111111-1-1-1-1−i−iii11-1-1-1-11111111-1-1-1−ii1-11-11-1-1-1-111-1-1-1-1-1-1−i−iii-1-1-1-1−i−iiiiiii−i−i−i−i1111−i−iii-111−iiii−i−i
χ91111111111111111-11-11-11-1111111111ii−i−i1111-1-111-1-1111111-11i−i11-11-11-11-1-1-1-1-111ii−i−i1111ii−i−i1111ii−i−iii−i−iii−i−i-1-1-1-1-1i−i-1-1i−ii−i
χ101111111111111111-11-11-11-1111111111ii−i−i-1-1-1-1-1-111-1-1111111-11i−i-1-1-11-11-11-1-1-1-1-111ii−i−i-1-1-1-1ii−i−i-1-1-1-1−i−iii−i−iiiii−i−i1111-1i−i11−ii−ii
χ111111111111111111-11-11-11-1111111111−i−iii1111-1-111-1-1111111-11−ii11-11-11-11-1-1-1-1-111−i−iii1111−i−iii1111−i−iii−i−iii−i−iii-1-1-1-1-1−ii-1-1−ii−ii
χ121111111111111111-11-11-11-1111111111−i−iii-1-1-1-1-1-111-1-1111111-11−ii-1-1-11-11-11-1-1-1-1-111−i−iii-1-1-1-1−i−iii-1-1-1-1ii−i−iii−i−i−i−iii1111-1−ii11i−ii−i
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-1-11111-1-1−i−iii−i−iii1−ii−ii-111-1
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−iii11-1-1-1-111−i−iiiii−i−i1−iii−i1-1-11
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−i11-1-1-1-111ii−i−i−i−iii1i−i−ii1-1-11
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-1-11111-1-1ii−i−iii−i−i1i−ii−i-111-1
χ17111111111-1111111111111111-1-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1
χ18111111111-1111111111111111-1-1-1-11111111-1-1-1-1111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111
χ19111111111-1111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-111-1-111-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11111
χ20111111111-1111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ21111111111-11111111-11-11-11-11-1-1-1-11111111ii−i−i11-1-1-1-1-1-1-1-111-11-1-1−ii1-11-11-1-1-1-1-1-111-1-1-1-1−i−iii1111ii−i−iiiii−i−i−i−i-1-1-1-1ii−i−i111−ii−i−iii
χ22111111111-11111111-11-11-11-11-1-1-1-11111111−i−iii11-1-1-1-1-1-1-1-111-11-1-1i−i1-11-11-1-1-1-1-1-111-1-1-1-1ii−i−i1111−i−iii−i−i−i−iiiii-1-1-1-1−i−iii111i−iii−i−i
χ23111111111-11111111-11-11-11-11-1-1-1-1111-1-1-1-1ii−i−i11-1-1-1-1-1-1-1-111-1111−ii1-11-11-1-1-1-1-1-1111111−i−iii-1-1-1-1ii−i−i−i−i−i−iiiii1111ii−i−i1-1-1−iiii−i−i
χ24111111111-11111111-11-11-11-11-1-1-1-1111-1-1-1-1−i−iii11-1-1-1-1-1-1-1-111-1111i−i1-11-11-1-1-1-1-1-1111111ii−i−i-1-1-1-1−i−iiiiiii−i−i−i−i1111−i−iii1-1-1i−i−i−iii
χ25111111111-1111111-11-11-11-111-1-1-1-1111ii−i−i1111-1-111-1-1-1-1-1-1111-1−ii-1-1-11-11-11-1-1-111-1-1−i−iii-1-1-1-1ii−i−i1111ii−i−iii−i−iii−i−i-1-1-1-11−ii11−ii−ii
χ26111111111-1111111-11-11-11-111-1-1-1-1111ii−i−i-1-1-1-1-1-111-1-1-1-1-1-1111-1−ii11-11-11-11-1-1-111-1-1−i−iii1111ii−i−i-1-1-1-1−i−iii−i−iiiii−i−i11111−ii-1-1i−ii−i
χ27111111111-1111111-11-11-11-111-1-1-1-1111−i−iii1111-1-111-1-1-1-1-1-1111-1i−i-1-1-11-11-11-1-1-111-1-1ii−i−i-1-1-1-1−i−iii1111−i−iii−i−iii−i−iii-1-1-1-11i−i11i−ii−i
χ28111111111-1111111-11-11-11-111-1-1-1-1111−i−iii-1-1-1-1-1-111-1-1-1-1-1-1111-1i−i11-11-11-11-1-1-111-1-1ii−i−i1111−i−iii-1-1-1-1ii−i−iii−i−i−i−iii11111i−i-1-1−ii−ii
χ29111111111-1111111-1-1-1-1-1-1-1-11-1-1-1-1111ii−i−iii−i−i-1-1-1-111-1-1-1-11111−ii−ii-1-1-1-1-1-11111111−i−iii−i−iiiii−i−iii−i−i-1-11111-1-1−i−iii−i−iii-1i−ii−i1-1-11
χ30111111111-1111111-1-1-1-1-1-1-1-11-1-1-1-1111ii−i−i−i−iii-1-1-1-111-1-1-1-11111−iii−i-1-1-1-1-1-11111111−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-1i−i−ii-111-1
χ31111111111-1111111-1-1-1-1-1-1-1-11-1-1-1-1111−i−iiiii−i−i-1-1-1-111-1-1-1-11111i−i−ii-1-1-1-1-1-11111111ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-1−iii−i-111-1
χ32111111111-1111111-1-1-1-1-1-1-1-11-1-1-1-1111−i−iii−i−iii-1-1-1-111-1-1-1-11111i−ii−i-1-1-1-1-1-11111111ii−i−iii−i−i−i−iii−i−iii-1-11111-1-1ii−i−iii−i−i-1−ii−ii1-1-11
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χ35222-2-22222022-2-2-2-22-22-2-22-22200002220000000022-2-2-2-20000-2-20000002-2-22-22-222000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000
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χ4622-22-222220-2-222-2-2-222-2-2-22220000-2-22-222-2000022-2-22200002-2000000-22-2-222-2-22000000000000-222-2000000000000-222-20000000000000
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χ89888-8-88-28-208-2-82-8208080-80-8-20000-2-2-20000000000-2-2000000220000000-20202000000000000000000000000000000000000000000000000
χ90888-8-88-28-208-2-82-820-80-80808-20000-2-2-200000000002200000022000000020-20-2000000000000000000000000000000000000000000000000
χ91888-8-8-28-280-282-82-88080-80-80-20000-2-2-200000000-2-20000000022000000-202020000000000000000000000000000000000000000000000000
χ92888-8-8-28-280-282-82-8-80-808080-20000-2-2-20000000022000000002200000020-20-20000000000000000000000000000000000000000000000000
χ9388-88-88-28-20-828-2-82080-80-808-2000022-2000000000022000000-220000000-2020-2000000000000000000000000000000000000000000000000
χ9488-88-88-28-20-828-2-820-808080-8-2000022-20000000000-2-2000000-22000000020-202000000000000000000000000000000000000000000000000
χ9588-8-88-28-2802-82-8-2880-80-8080-2000022-20000000022000000002-2000000-2020-20000000000000000000000000000000000000000000000000
χ9688-8-88-28-2802-82-8-28-808080-80-2000022-200000000-2-2000000002-200000020-2020000000000000000000000000000000000000000000000000
χ978-800088-8-80000000000000008000000-80000000000008-8000000000000000000000000000000000000000000000000000000000000000000
χ988-800088-8-80000000000000008000000-8000000000000-88000000000000000000000000000000000000000000000000000000000000000000
χ991616161616-4-4-4-416-4-4-4-4-4-4000000001-4-4-4-411100000000000000111111000000000000000000000000000000000000000000000000000000000000
χ1001616161616-4-4-4-4-16-4-4-4-4-4-4000000001444411100000000000000-1-1-1-111000000000000000000000000000000000000000000000000000000000000
χ101161616-16-16-4-4-4-40-4-444440000000010000111000000000000005-5-55-1-1000000000000000000000000000000000000000000000000000000000000
χ102161616-16-16-4-4-4-40-4-44444000000001000011100000000000000-555-5-1-1000000000000000000000000000000000000000000000000000000000000
χ1031616-1616-16-4-4-4-4044-4-44400000000145−4500-1-1100000000000000−5−5551-1000000000000000000000000000000000000000000000000000000000000
χ1041616-1616-16-4-4-4-4044-4-444000000001−454500-1-110000000000000055−5−51-1000000000000000000000000000000000000000000000000000000000000
χ1051616-16-1616-4-4-4-404444-4-40000000010045−45-1-1100000000000000−55−55-11000000000000000000000000000000000000000000000000000000000000
χ1061616-16-1616-4-4-4-404444-4-400000000100−4545-1-11000000000000005−55−5-11000000000000000000000000000000000000000000000000000000000000
χ10716-1600016-4-164000000000000000-40000004000000000045−4500000000000000000000000000000000000000000000000000000000000000000000
χ10816-1600016-4-164000000000000000-400000040000000000−454500000000000000000000000000000000000000000000000000000000000000000000
χ10916-16000-4164-16000000000000000-400000040000000045−450000000000000000000000000000000000000000000000000000000000000000000000
χ11016-16000-4164-16000000000000000-4000000400000000−45450000000000000000000000000000000000000000000000000000000000000000000000
χ11132-32000-8-8880000000000000002000010-10-200000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11232-32000-8-88800000000000000020000-1010-200000000000000000000000000000000000000000000000000000000000000000000000000000000

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