Finite Group Databasebeta

← Group #13026420

Character table — Group #13026420

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444444444444488888888888888881010101016161616161616162020202020202020202040408080808080808080
order12442422244451010102020202088881010101010102020202020208888404040404040404022448888884444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ511111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1i−ii−ii−ii−i
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−ii−ii−ii−ii
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111-1-11
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-111-1
χ91111111-1-11-1-11111111111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111i−ii−i−ii−ii
χ101111111-1-11-1-11111111111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111−ii−iii−ii−i
χ111111111-1-11-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1-11-111-1
χ121111111-1-11-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-111-11-1-11
χ131111111-1-11-1-111111111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ141111111-1-11-1-111111111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111
χ151111111-1-11-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111ii−i−i−i−iii
χ161111111-1-11-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111−i−iiiii−i−i
χ17222222-200-20022222222002-2-2-20000-2-200002222000022-2-22-2-22-2-200000000000000
χ18222222-200-20022222222002-2-2-20000-2-20000-2-2-2-2000022-2-2-222-22200000000000000
χ19222222-200-2002222222200-22-2-20000-2-2000022220000-2-222-222-2-2-200000000000000
χ20222222-200-2002222222200-22-2-20000-2-20000-2-2-2-20000-2-2222-2-222200000000000000
χ2122-2-22-2222-2-2-22222-2-2-2-20000222222-2-2-2-2-2-20000000000002-22-20000002-200000000
χ2222-2-22-2222-2-2-22222-2-2-2-20000222222-2-2-2-2-2-2000000000000-22-22000000-2200000000
χ2322-2-22-22-2-2-2222222-2-2-2-2000022-2-2-2-2-2-222220000000000002-22-2000000-2200000000
χ2422-2-22-22-2-2-2222222-2-2-2-2000022-2-2-2-2-2-22222000000000000-22-220000002-200000000
χ2522-2-22-2-2002002222-2-2-2-22i−2i00-2-2000022000000002i2i−2i−2i000022-2-2002i2i−2i−2i0000000000
χ2622-2-22-2-2002002222-2-2-2-22i−2i00-2-2000022000000002i2i−2i−2i0000-2-22200−2i−2i2i2i0000000000
χ2722-2-22-2-2002002222-2-2-2-2−2i2i00-2-200002200000000−2i−2i2i2i000022-2-200−2i−2i2i2i0000000000
χ2822-2-22-2-2002002222-2-2-2-2−2i2i00-2-200002200000000−2i−2i2i2i0000-2-222002i2i−2i−2i0000000000
χ29444444444444-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000
χ30444444444444-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000
χ314444444-4-44-4-4-1-1-1-1-1-1-1-144-4-4-1-11111-1-111110000-1-1-1-1111100000000000000000000
χ324444444-4-44-4-4-1-1-1-1-1-1-1-1-4-444-1-11111-1-1111100001111-1-1-1-100000000000000000000
χ33444444-400-400-1-1-1-1-1-1-1-1004-41155−5−51155−5−500005−55−5-1-11100000000000000000000
χ34444444-400-400-1-1-1-1-1-1-1-1004-411−5−55511−5−5550000−55−55-1-11100000000000000000000
χ35444444-400-400-1-1-1-1-1-1-1-100-441155−5−51155−5−50000−55−5511-1-100000000000000000000
χ36444444-400-400-1-1-1-1-1-1-1-100-4411−5−55511−5−55500005−55−511-1-100000000000000000000
χ374444-4-40000004-4-4444-4-4000000000000000000000000000000004i−4i00000000000000
χ384444-4-40000004-4-4444-4-400000000000000000000000000000000−4i4i00000000000000
χ3944-4-44-4444-4-4-4-1-1-1-111110000-1-1-1-1-1-11111110000i5−i5−i5i5i5−i5i5−i500000000000000000000
χ4044-4-44-4444-4-4-4-1-1-1-111110000-1-1-1-1-1-11111110000−i5i5i5−i5−i5i5−i5i500000000000000000000
χ4144-4-44-44-4-4-444-1-1-1-111110000-1-1111111-1-1-1-10000i5−i5−i5i5−i5i5−i5i500000000000000000000
χ4244-4-44-44-4-4-444-1-1-1-111110000-1-1111111-1-1-1-10000−i5i5i5−i5i5−i5i5−i500000000000000000000
χ4344-4-44-4-400400-1-1-1-111114i−4i001155−5−5-1-1−5−5550000−i−iiii5−i5−i5i500000000000000000000
χ4444-4-44-4-400400-1-1-1-111114i−4i0011−5−555-1-155−5−50000−i−iii−i5i5i5−i500000000000000000000
χ4544-4-44-4-400400-1-1-1-11111−4i4i001155−5−5-1-1−5−5550000ii−i−i−i5i5i5−i500000000000000000000
χ4644-4-44-4-400400-1-1-1-11111−4i4i0011−5−555-1-155−5−50000ii−i−ii5−i5−i5i500000000000000000000
χ4744-4-4-440000004-4-44-4-444000000000000000044-4-40000000000000000000000000000
χ4844-4-4-440000004-4-44-4-4440000000000000000-4-4440000000000000000000000000000
χ494-44i−4i0002-202i−2i400-44i−4i000000002-22-2002i−2i2i−2i2i2−2i222−2200000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ504-44i−4i0002-202i−2i400-44i−4i000000002-22-2002i−2i2i−2i−2i22i2−2222000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ514-44i−4i000-220−2i2i400-44i−4i00000000-22-2200−2i2i−2i2i2i2−2i222−22000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ524-44i−4i000-220−2i2i400-44i−4i00000000-22-2200−2i2i−2i2i−2i22i2−222200000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ534-4−4i4i0002-20−2i2i400-4−4i4i000000002-22-200−2i2i−2i2i2i2−2i2−222200000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ544-4−4i4i0002-20−2i2i400-4−4i4i000000002-22-200−2i2i−2i2i−2i22i222−22000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ554-4−4i4i000-2202i−2i400-4−4i4i00000000-22-22002i−2i2i−2i2i2−2i2−2222000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ564-4−4i4i000-2202i−2i400-4−4i4i00000000-22-22002i−2i2i−2i−2i22i222−2200000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ578888-8-8000000-222-2-2-222000025−25000025−25000000000000000000000000000000000000
χ588888-8-8000000-222-2-2-2220000−25250000−2525000000000000000000000000000000000000
χ5988-8-8-88000000-222-222-2-2000025−250000−2525000000000000000000000000000000000000
χ6088-8-8-88000000-222-222-2-20000−2525000025−25000000000000000000000000000000000000
χ618-88i−8i0004-404i−4i-225−252−2i2i2i5−2i5000000−1+51−5−1−51+500−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000000000
χ628-88i−8i0004-404i−4i-2−25252−2i2i−2i52i5000000−1−51+5−1+51−500−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000000000
χ638-88i−8i000-440−4i4i-225−252−2i2i2i5−2i50000001−5−1+51+5−1−5002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000000000
χ648-88i−8i000-440−4i4i-2−25252−2i2i−2i52i50000001+5−1−51−5−1+5002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000000000
χ658-8−8i8i0004-40−4i4i-225−2522i−2i−2i52i5000000−1+51−5−1−51+5002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000000000
χ668-8−8i8i0004-40−4i4i-2−252522i−2i2i5−2i5000000−1−51+5−1+51−5002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000000000
χ678-8−8i8i000-4404i−4i-225−2522i−2i−2i52i50000001−5−1+51+5−1−500−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000000000
χ688-8−8i8i000-4404i−4i-2−252522i−2i2i5−2i50000001+5−1−51−5−1+500−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000000000

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