Finite Group Databasebeta

← Group #72223190

Character table — Group #72223190

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size111122224444444444444444488888888888888888888888888888888888888882020202020202020252525254040404040404040404040404040404050505050100100100100100100100100100200200200200
order1222444445510101010101020202020202020205510101010101020202020202020202020202020202020202020202020202020202020202020208888888822224040404040404040404040404040404044444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1iiii−i−i−i−i−i−iii
χ611111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1−i−i−i−iiiiiii−i−i
χ711111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1
χ811111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111
χ91111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i1111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11ii−i−iii−i−i1-11-1
χ101111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i1111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11−i−iii−i−iii-11-11
χ111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1111-111-1-1-1-111−iii−i
χ121111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-11111-1-1i−i−ii
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1111-111-1-1-1-111i−i−ii
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-11111-1-1−iii−i
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii1111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11ii−i−iii−i−i-11-11
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii1111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11−i−iii−i−iii1-11-1
χ17222222-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-200000000222200000000000000002-2-22-2000000000000
χ18222222-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000-222-22000000000000
χ192222-2-222-2222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000022220000000000000000-222-2-2000000000000
χ202222-2-222-2222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000-2-2-2-200000000000000002-2-222000000000000
χ2122-2-2002-202222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000002222-2-2-2-20000000022-2-2000000000000000002-2002−22−22−22−20000
χ2222-2-2002-202222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000002222-2-2-2-20000000022-2-2000000000000000002-200−22−22−22−220000
χ2322-2-2002-202222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000002222-2-2-2-200000000-2-22200000000000000000-2200i2−i2i2−i2−i2i2−i2i20000
χ2422-2-2002-202222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000002222-2-2-2-200000000-2-22200000000000000000-2200−i2i2−i2i2i2−i2i2−i20000
χ2522-2-200-2202222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000-2-2-2-222220000000022-2-200000000000000000-2200i2−i2−i2i2i2−i2−i2i20000
χ2622-2-200-2202222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000-2-2-2-222220000000022-2-200000000000000000-2200−i2i2i2−i2−i2i2i2−i20000
χ2722-2-200-2202222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000-2-2-2-2222200000000-2-222000000000000000002-2002−2−22−222−20000
χ2822-2-200-2202222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000-2-2-2-2222200000000-2-222000000000000000002-200−222−22−2−220000
χ292-22-22-200022-2-222-2-20000000022-2-222-2-2000022-2-2000000002222-2-2-2-200000000i2−i2i2−i2i2−i2i2−i22-22-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-20020000000000000
χ302-22-22-200022-2-222-2-20000000022-2-222-2-2000022-2-2000000002222-2-2-2-200000000i2−i2i2−i2−i2i2−i2i2-22-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2200-20000000000000
χ312-22-22-200022-2-222-2-20000000022-2-222-2-2000022-2-2000000002222-2-2-2-200000000−i2i2−i2i2i2−i2i2−i2-22-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2200-20000000000000
χ322-22-22-200022-2-222-2-20000000022-2-222-2-2000022-2-2000000002222-2-2-2-200000000−i2i2−i2i2−i2i2−i2i22-22-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-20020000000000000
χ332-22-2-2200022-2-222-2-20000000022-2-222-2-20000-2-22200000000-2-2-2-22222000000002−2−222−2−222-22-222−2−2−2−22222−2−2−2−222200-20000000000000
χ342-22-2-2200022-2-222-2-20000000022-2-222-2-20000-2-22200000000-2-2-2-22222000000002−2−22−222−2-22-2222−2−2−2−222−2−22222−2−2-20020000000000000
χ352-22-2-2200022-2-222-2-20000000022-2-222-2-20000-2-22200000000-2-2-2-2222200000000−222−22−2−22-22-22−2−22222−2−222−2−2−2−222-20020000000000000
χ362-22-2-2200022-2-222-2-20000000022-2-222-2-20000-2-22200000000-2-2-2-2222200000000−222−2−222−22-22-2−2−22222−2−2−2−22222−2−2200-20000000000000
χ374444444444-14-14-14-144-1-144-1-1-1-1-1-1-1-1-1-144-1-14-14-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100004444000000000000-1-1-1-1-1-1-1-100000000000000000
χ384444444444-14-14-14-144-1-144-1-1-1-1-1-1-1-1-1-144-1-14-14-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4-4-4-40000000000001111111100000000000000000
χ39444444444-14-14-14-14-1-144-1-144-1-1-1-1-1-1-1-1-1-144-14-14-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1444400000000-1-1-1-1-1-1-1-10000000000000000000000000
χ40444444444-14-14-14-14-1-144-1-144-1-1-1-1-1-1-1-1-1-144-14-14-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-400000000111111110000000000000000000000000
χ41444444-4-4-44-14-14-14-1-4-411-4-411-1-1-1-1-1-1-1-1-4-4114-14-111111111-1-1-1-1-1-1-1-11111111100000000000000000000i5−i5i5−i5i5−i5i5−i500000000000000000
χ42444444-4-4-44-14-14-14-1-4-411-4-411-1-1-1-1-1-1-1-1-4-4114-14-111111111-1-1-1-1-1-1-1-11111111100000000000000000000−i5i5−i5i5−i5i5−i5i500000000000000000
χ43444444-4-4-4-14-14-14-1411-4-411-4-4-1-1-1-1-1-1-1-111-4-4-14-1411111111-1-1-1-1-1-1-1-111111111000000000000i5−i5i5−i5i5−i5i5−i50000000000000000000000000
χ44444444-4-4-4-14-14-14-1411-4-411-4-4-1-1-1-1-1-1-1-111-4-4-14-1411111111-1-1-1-1-1-1-1-111111111000000000000−i5i5−i5i5−i5i5−i5i50000000000000000000000000
χ454444-4-444-44-14-14-14-144-1-144-1-1-1-1-1-1-1-1-1-1-4-411-41-411111111111111111-1-1-1-1-1-1-1-1000000000000000000005−55−5−55−5500000000000000000
χ464444-4-444-44-14-14-14-144-1-144-1-1-1-1-1-1-1-1-1-1-4-411-41-411111111111111111-1-1-1-1-1-1-1-100000000000000000000−55−555−55−500000000000000000
χ474444-4-444-4-14-14-14-14-1-144-1-144-1-1-1-1-1-1-1-111-4-41-41-41111111111111111-1-1-1-1-1-1-1-10000000000005−55−5−55−550000000000000000000000000
χ484444-4-444-4-14-14-14-14-1-144-1-144-1-1-1-1-1-1-1-111-4-41-41-41111111111111111-1-1-1-1-1-1-1-1000000000000−55−555−55−50000000000000000000000000
χ494444-4-4-4-444-14-14-14-1-4-411-4-411-1-1-1-1-1-1-1-144-1-1-41-41-1-1-1-1-1-1-1-1111111111111111100004i4i−4i−4i000000000000−i−i−i−iiiii00000000000000000
χ504444-4-4-4-444-14-14-14-1-4-411-4-411-1-1-1-1-1-1-1-144-1-1-41-41-1-1-1-1-1-1-1-111111111111111110000−4i−4i4i4i000000000000iiii−i−i−i−i00000000000000000
χ514444-4-4-4-44-14-14-14-1411-4-411-4-4-1-1-1-1-1-1-1-1-1-1441-41-4-1-1-1-1-1-1-1-111111111111111114i4i−4i−4i00000000−i−i−i−iiiii0000000000000000000000000
χ524444-4-4-4-44-14-14-14-1411-4-411-4-4-1-1-1-1-1-1-1-1-1-1441-41-4-1-1-1-1-1-1-1-11111111111111111−4i−4i4i4i00000000iiii−i−i−i−i0000000000000000000000000
χ534-44-44-40004-1-414-1-4100i5−i500i5−i5-1-111-1-11100i5−i54-1-41i5i5i5i5−i5−i5−i5−i5-1-1-1-11111i5i5−i5−i5i5i5−i5−i500002i2−2i22i2−2i2000000000000ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ3900000000000000000
χ544-44-44-40004-1-414-1-4100i5−i500i5−i5-1-111-1-11100i5−i54-1-41i5i5i5i5−i5−i5−i5−i5-1-1-1-11111i5i5−i5−i5i5i5−i5−i50000−2i22i2−2i22i2000000000000−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ3900000000000000000
χ554-44-44-40004-1-414-1-4100−i5i500−i5i5-1-111-1-11100−i5i54-1-41−i5−i5−i5−i5i5i5i5i5-1-1-1-11111−i5−i5i5i5−i5−i5i5i500002i2−2i22i2−2i2000000000000ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ2900000000000000000
χ564-44-44-40004-1-414-1-4100−i5i500−i5i5-1-111-1-11100−i5i54-1-41−i5−i5−i5−i5i5i5i5i5-1-1-1-11111−i5−i5i5i5−i5−i5i5i50000−2i22i2−2i22i2000000000000−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ2900000000000000000
χ574-44-44-4000-141-4-141-4i5−i500i5−i500-1-111-1-111i5−i500-141-4i5i5−i5−i5i5i5−i5−i5-1-1-1-11111i5−i5i5−i5i5−i5i5−i52i2−2i22i2−2i200000000ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ390000000000000000000000000
χ584-44-44-4000-141-4-141-4i5−i500i5−i500-1-111-1-111i5−i500-141-4i5i5−i5−i5i5i5−i5−i5-1-1-1-11111i5−i5i5−i5i5−i5i5−i5−2i22i2−2i22i200000000−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ390000000000000000000000000
χ594-44-44-4000-141-4-141-4−i5i500−i5i500-1-111-1-111−i5i500-141-4−i5−i5i5i5−i5−i5i5i5-1-1-1-11111−i5i5−i5i5−i5i5−i5i52i2−2i22i2−2i200000000ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ290000000000000000000000000
χ604-44-44-4000-141-4-141-4−i5i500−i5i500-1-111-1-111−i5i500-141-4−i5−i5i5i5−i5−i5i5i5-1-1-1-11111−i5i5−i5i5−i5i5−i5i5−2i22i2−2i22i200000000−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ290000000000000000000000000
χ614-44-4-440004-1-414-1-4100i5−i500i5−i5-1-111-1-11100−i5i5-414-1−i5−i5−i5−i5i5i5i5i51111-1-1-1-1i5i5−i5−i5i5i5−i5−i5000022−22−2222000000000000−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ3900000000000000000
χ624-44-4-440004-1-414-1-4100i5−i500i5−i5-1-111-1-11100−i5i5-414-1−i5−i5−i5−i5i5i5i5i51111-1-1-1-1i5i5−i5−i5i5i5−i5−i50000−222222−22000000000000ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ3900000000000000000
χ634-44-4-440004-1-414-1-4100−i5i500−i5i5-1-111-1-11100i5−i5-414-1i5i5i5i5−i5−i5−i5−i51111-1-1-1-1−i5−i5i5i5−i5−i5i5i5000022−22−2222000000000000ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ2900000000000000000
χ644-44-4-440004-1-414-1-4100−i5i500−i5i5-1-111-1-11100i5−i5-414-1i5i5i5i5−i5−i5−i5−i51111-1-1-1-1−i5−i5i5i5−i5−i5i5i50000−222222−22000000000000−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ2900000000000000000
χ654-44-4-44000-141-4-141-4i5−i500i5−i500-1-111-1-111−i5i5001-4-14−i5−i5i5i5−i5−i5i5i51111-1-1-1-1i5−i5i5−i5i5−i5i5−i522−22−222200000000−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ390000000000000000000000000
χ664-44-4-44000-141-4-141-4i5−i500i5−i500-1-111-1-111−i5i5001-4-14−i5−i5i5i5−i5−i5i5i51111-1-1-1-1i5−i5i5−i5i5−i5i5−i5−222222−2200000000ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ390000000000000000000000000
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χ1058-8-8800000-2-22222-2-22i5−2i5−2i52i5−2i52i52i5−2i5-232-32-3-2300000000005-5-5500−2i52i5i5−i52i5−2i5−i5i50i5−i500−i5i50000000000000000000000000000000000000000000000
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χ1078-8-8800000-2-22222-2-2−2i52i52i5−2i52i5−2i5−2i52i5-232-32-3-2300000000005-5-55002i5−2i5−i5i5−2i52i5i5−i50−i5i500i5−i50000000000000000000000000000000000000000000000
χ1088-8-8800000-2-22222-2-2−2i52i52i5−2i52i5−2i5−2i52i5-232-32-3-230000000000-555-500−2i52i5i5−i52i5−2i5−i5i50−i5i500i5−i50000000000000000000000000000000000000000000000
χ1098-8-8800000-2-22222-2-2−2i52i5−2i52i52i5−2i52i5−2i53-2-32-323-2000000005-50000-55i5−i52i5−2i5−i5i5−2i52i5i500−i5−i500i5000000000000000000000000000000000000000000000
χ1108-8-8800000-2-22222-2-2−2i52i5−2i52i52i5−2i52i5−2i53-2-32-323-200000000-5500005-5−i5i5−2i52i5i5−i52i5−2i5i500−i5−i500i5000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.