Finite Group Databasebeta

← Group #13104092

Character table — Group #13104092

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111444444444888888888888888888881010101020202525252540404040404040405050505050505050100100100100100
order122225510101010101055101010101010101010101010101010101010444444444420202020202020208888888848888
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ311111111111111111111111111111111111-1-11-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1ii−i−i
χ411111111111111111111111111111111111-1-11-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1−i−iii
χ5111111111111111111111111111111111-1-111-11-1-1-1-1-1-1-1-11111ii−i−iii−i−i-1i−ii−i
χ6111111111111111111111111111111111-1-111-11-1-1-1-1-1-1-1-11111−i−iii−i−iii-1−ii−ii
χ7111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ8111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11-111-1
χ91111-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-111111111-1-1-1-1-1
χ101111-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-11111
χ111111-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-111-1-1-1-111iiii−i−i−i−i1−i−iii
χ121111-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-111-1-1-1-111−i−i−i−iiiii1ii−i−i
χ131111-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111-1-1ii−i−iii−i−i1−ii−ii
χ141111-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111-1-1−i−iii−i−iii1i−ii−i
χ151111-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-111-1-111-1
χ161111-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-11-1-11
χ1722-2-2022-2-222-2-222000022-2-2-2-2000000000000002i2i−2i−2i0000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000
χ1822-2-2022-2-222-2-222000022-2-2-2-2000000000000002i2i−2i−2i00000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000
χ1922-2-2022-2-222-2-222000022-2-2-2-200000000000000−2i−2i2i2i0000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000
χ2022-2-2022-2-222-2-222000022-2-2-2-200000000000000−2i−2i2i2i00000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000
χ212-22-2022-2-2-2-222220000-2-222-2-2000000000000002i−2i2i−2i00000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000
χ222-22-2022-2-2-2-222220000-2-222-2-2000000000000002i−2i2i−2i000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000
χ232-22-2022-2-2-2-222220000-2-222-2-200000000000000−2i2i−2i2i00000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000
χ242-22-2022-2-2-2-222220000-2-222-2-200000000000000−2i2i−2i2i000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000
χ252-2-2202222-2-2-2-2220000-2-2-2-222000000002i−2i2i−2i002-2-222i−2i002i−2i000000000000000
χ262-2-2202222-2-2-2-2220000-2-2-2-222000000002i−2i−2i2i00-222-22i−2i00−2i2i000000000000000
χ272-2-2202222-2-2-2-2220000-2-2-2-22200000000−2i2i2i−2i00-222-2−2i2i002i−2i000000000000000
χ282-2-2202222-2-2-2-2220000-2-2-2-22200000000−2i2i−2i2i002-2-22−2i2i00−2i2i000000000000000
χ29444444-14-14-14-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100440400000000-1-1-1-10000000000000
χ30444444-14-14-14-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-4-40-40000000011110000000000000
χ3144444-14-14-14-14-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-14400400000-1-1-1-100000000000000000
χ3244444-14-14-14-14-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-400-400000111100000000000000000
χ334444-44-14-14-14-1-1-1-4-411-1-1-1-1-1-11111111100440-400000000-1-1110000000000000
χ344444-44-14-14-14-1-1-1-4-411-1-1-1-1-1-11111111100-4-4040000000011-1-10000000000000
χ354444-4-14-14-14-14-1-111-4-4-1-1-1-1-1-1111111114400-400000-1-11100000000000000000
χ364444-4-14-14-14-14-1-111-4-4-1-1-1-1-1-111111111-4-40040000011-1-100000000000000000
χ374-4-4404-14-1-41-41-1-1005−51111-1-15555−5−5−5−5004i−4i0000000000−iii5−i50000000000000
χ384-4-4404-14-1-41-41-1-1005−51111-1-15555−5−5−5−500−4i4i0000000000i−i−i5i50000000000000
χ394-4-4404-14-1-41-41-1-100−551111-1-1−5−5−5−55555004i−4i0000000000−ii−i5i50000000000000
χ404-4-4404-14-1-41-41-1-100−551111-1-1−5−5−5−5555500−4i4i0000000000i−ii5−i50000000000000
χ414-4-440-14-141-41-4-1-15−5001111-1-155−5−555−5−54i−4i00000000−iii5−i500000000000000000
χ424-4-440-14-141-41-4-1-15−5001111-1-155−5−555−5−5−4i4i00000000i−i−i5i500000000000000000
χ434-4-440-14-141-41-4-1-1−55001111-1-1−5−555−5−5554i−4i00000000−ii−i5i500000000000000000
χ444-4-440-14-141-41-4-1-1−55001111-1-1−5−555−5−555−4i4i00000000i−ii5−i500000000000000000
χ4588888-2-2-2-2-2-2-2-23-2-2-2-2-23-23-23-233-2-2-2-2330000000000000000000000000000000
χ4688888-2-2-2-2-2-2-2-2-23-2-2-2-2-23-23-23-2-23333-2-20000000000000000000000000000000
χ478888-8-2-2-2-2-2-2-2-23-222223-23-23-2-3-32222-3-30000000000000000000000000000000
χ488888-8-2-2-2-2-2-2-2-2-232222-23-23-2322-3-3-3-3220000000000000000000000000000000
χ4988-8-808-2-828-2-82-2-20000-2-22222000000000000000000000000000000000000000
χ5088-8-80-282-8-282-8-2-20000-2-22222000000000000000000000000000000000000000
χ5188-8-80-2-222-2-2223-200003-2-32-325-500005-50000000000000000000000000000000
χ5288-8-80-2-222-2-2223-200003-2-32-32-550000-550000000000000000000000000000000
χ5388-8-80-2-222-2-222-230000-232-32-3005-55-5000000000000000000000000000000000
χ5488-8-80-2-222-2-222-230000-232-32-300-55-55000000000000000000000000000000000
χ558-88-808-2-82-828-2-2-2000022-2-222000000000000000000000000000000000000000
χ568-88-80-282-82-8-28-2-2000022-2-222000000000000000000000000000000000000000
χ578-88-80-2-22222-2-23-20000-323-2-325−525−25−2525−550000000000000000000000000000000
χ588-88-80-2-22222-2-23-20000-323-2-32−55−252525−255−50000000000000000000000000000000
χ598-88-80-2-22222-2-2-2300002-3-232-325−25−555−5−25250000000000000000000000000000000
χ608-88-80-2-22222-2-2-2300002-3-232-3−25255−5−5525−250000000000000000000000000000000
χ618-8-880-2-2-2-222223-225−2525−25-32-323-2−5−50000550000000000000000000000000000000
χ628-8-880-2-2-2-222223-2−2525−2525-32-323-2550000−5−50000000000000000000000000000000
χ638-8-880-2-2-2-22222-2325−25−25252-32-3-230055−5−5000000000000000000000000000000000
χ648-8-880-2-2-2-22222-23−252525−252-32-3-2300−5−555000000000000000000000000000000000

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