Finite Group Databasebeta

← Group #13026557

Character table — Group #13026557

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444444444444488888888888888881010101016161616161616162020202020202020202040408080808080808080
order12442424588881010102020202044881010202040404040404040404444202020204040404022444488888844448888
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
χ511111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−i−i−iii
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−i
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111
χ9111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-11-11-11-11-1
χ10111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-11-11-11-11
χ11111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111i−i−iii−i−ii
χ12111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111−iii−i−iii−i
χ13111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111i−i−ii−iii−i
χ14111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111−iii−ii−i−ii
χ15111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-11-11-1-11-11
χ16111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-11-111-11-1
χ17222222-2-22000022222222-200-2-2-2-200000000222222-2-200002-2-2-22-200000000000000
χ18222222-2-22000022222222-200-2-2-2-200000000-2-2-2-222-2-20000-2222-2200000000000000
χ19222222-2-2200002222222-2200-2-2-2-2000000002222-2-2220000-22-2-2-2200000000000000
χ20222222-2-2200002222222-2200-2-2-2-200000000-2-2-2-2-2-22200002-2222-200000000000000
χ2122-2-22-22-222i2i−2i−2i222-2-2-2-2000022-2-22i2i2i2i−2i−2i−2i−2i0000000000002-200-2200002i−2i00000000
χ2222-2-22-22-222i2i−2i−2i222-2-2-2-2000022-2-22i2i2i2i−2i−2i−2i−2i000000000000-22002-20000−2i2i00000000
χ2322-2-22-22-22−2i−2i2i2i222-2-2-2-2000022-2-2−2i−2i−2i−2i2i2i2i2i0000000000002-200-220000−2i2i00000000
χ2422-2-22-22-22−2i−2i2i2i222-2-2-2-2000022-2-2−2i−2i−2i−2i2i2i2i2i000000000000-22002-200002i−2i00000000
χ2522-2-22-2-2220000222-2-2-2-2002i−2i-2-22200000000000000002i2i−2i−2i2200-2-22i2i−2i−2i0000000000
χ2622-2-22-2-2220000222-2-2-2-2002i−2i-2-22200000000000000002i2i−2i−2i-2-20022−2i−2i2i2i0000000000
χ2722-2-22-2-2220000222-2-2-2-200−2i2i-2-2220000000000000000−2i−2i2i2i2200-2-2−2i−2i2i2i0000000000
χ2822-2-22-2-2220000222-2-2-2-200−2i2i-2-2220000000000000000−2i−2i2i2i-2-200222i2i−2i−2i0000000000
χ2944444444-14444-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000
χ3044444444-14444-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000
χ3144444444-1-4-4-4-4-1-1-1-1-1-1-144-4-4-1-1-1-1111111110000-1-1-1-1111100000000000000000000
χ3244444444-1-4-4-4-4-1-1-1-1-1-1-1-4-444-1-1-1-11111111100001111-1-1-1-100000000000000000000
χ33444444-4-4-10000-1-1-1-1-1-1-14-400111155−5−555−5−50000-1-1115−55−500000000000000000000
χ34444444-4-4-10000-1-1-1-1-1-1-14-4001111−5−555−5−5550000-1-111−55−5500000000000000000000
χ35444444-4-4-10000-1-1-1-1-1-1-1-4400111155−5−555−5−5000011-1-1−55−5500000000000000000000
χ36444444-4-4-10000-1-1-1-1-1-1-1-44001111−5−555−5−555000011-1-15−55−500000000000000000000
χ374444-4-400400004-4-4-4-4440000000000000000000000000000004i−4i0000000000000000
χ384444-4-400400004-4-4-4-444000000000000000000000000000000−4i4i0000000000000000
χ3944-4-44-44-4-14i4i−4i−4i-1-1-111110000-1-111−i−i−i−iiiii00005−55−5i5−i5−i5i500000000000000000000
χ4044-4-44-44-4-14i4i−4i−4i-1-1-111110000-1-111−i−i−i−iiiii0000−55−55−i5i5i5−i500000000000000000000
χ4144-4-44-44-4-1−4i−4i4i4i-1-1-111110000-1-111iiii−i−i−i−i00005−55−5−i5i5i5−i500000000000000000000
χ4244-4-44-44-4-1−4i−4i4i4i-1-1-111110000-1-111iiii−i−i−i−i0000−55−55i5−i5−i5i500000000000000000000
χ4344-4-44-4-44-10000-1-1-11111004i−4i11-1-1i5i5−i5−i5−i5−i5i5i500005−5−55−i−iii00000000000000000000
χ4444-4-44-4-44-10000-1-1-11111004i−4i11-1-1−i5−i5i5i5i5i5−i5−i50000−555−5−i−iii00000000000000000000
χ4544-4-44-4-44-10000-1-1-1111100−4i4i11-1-1i5i5−i5−i5−i5−i5i5i50000−555−5ii−i−i00000000000000000000
χ4644-4-44-4-44-10000-1-1-1111100−4i4i11-1-1−i5−i5i5i5i5i5−i5−i500005−5−55ii−i−i00000000000000000000
χ4744-4-4-4400400004-4-444-4-400000000000000004i4i−4i−4i0000000000000000000000000000
χ4844-4-4-4400400004-4-444-4-40000000000000000−4i−4i4i4i0000000000000000000000000000
χ494-44i−4i00004−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39-400004i−4i00000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392+2i−2−2i2−2i−2+2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ504-44i−4i00004−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39-400004i−4i00000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2−2i2+2i−2+2i2−2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ514-44i−4i000042ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39-400004i−4i000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392+2i−2−2i2−2i−2+2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ524-44i−4i000042ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39-400004i−4i000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2−2i2+2i−2+2i2−2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ534-4−4i4i00004−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37-40000−4i4i00000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372−2i−2+2i2+2i−2−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ544-4−4i4i00004−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37-40000−4i4i00000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2+2i2−2i−2−2i2+2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ554-4−4i4i000042ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37-40000−4i4i000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372−2i−2+2i2+2i−2−2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ564-4−4i4i000042ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37-40000−4i4i000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2+2i2−2i−2−2i2+2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ578888-8-800-20000-22222-2-2000025−2525−250000000000000000000000000000000000000000
χ588888-8-800-20000-22222-2-20000−2525−25250000000000000000000000000000000000000000
χ5988-8-8-8800-20000-222-2-222000025−25−25250000000000000000000000000000000000000000
χ6088-8-8-8800-20000-222-2-2220000−252525−250000000000000000000000000000000000000000
χ618-88i−8i0000-2−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ37−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ39225−252i5−2i5−2i2i000000002ζ21+2ζ29−2ζ21−2ζ292ζ13+2ζ37−2ζ13−2ζ372ζ31+2ζ39−2ζ31−2ζ392ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ628-88i−8i0000-2−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ37−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ392−2525−2i52i5−2i2i000000002ζ13+2ζ37−2ζ13−2ζ372ζ21+2ζ29−2ζ21−2ζ292ζ7+2ζ23−2ζ7−2ζ232ζ31+2ζ39−2ζ31−2ζ3900000000000000000000000000000000
χ638-88i−8i0000-24ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ374ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ39225−252i5−2i5−2i2i00000000−2ζ21−2ζ292ζ21+2ζ29−2ζ13−2ζ372ζ13+2ζ37−2ζ31−2ζ392ζ31+2ζ39−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ648-88i−8i0000-24ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ374ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ392−2525−2i52i5−2i2i00000000−2ζ13−2ζ372ζ13+2ζ37−2ζ21−2ζ292ζ21+2ζ29−2ζ7−2ζ232ζ7+2ζ23−2ζ31−2ζ392ζ31+2ζ3900000000000000000000000000000000
χ658-8−8i8i0000-2−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ39−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ37225−25−2i52i52i−2i000000002ζ31+2ζ39−2ζ31−2ζ392ζ7+2ζ23−2ζ7−2ζ232ζ21+2ζ29−2ζ21−2ζ292ζ13+2ζ37−2ζ13−2ζ3700000000000000000000000000000000
χ668-8−8i8i0000-2−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ39−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ372−25252i5−2i52i−2i000000002ζ7+2ζ23−2ζ7−2ζ232ζ31+2ζ39−2ζ31−2ζ392ζ13+2ζ37−2ζ13−2ζ372ζ21+2ζ29−2ζ21−2ζ2900000000000000000000000000000000
χ678-8−8i8i0000-24ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ394ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ37225−25−2i52i52i−2i00000000−2ζ31−2ζ392ζ31+2ζ39−2ζ7−2ζ232ζ7+2ζ23−2ζ21−2ζ292ζ21+2ζ29−2ζ13−2ζ372ζ13+2ζ3700000000000000000000000000000000
χ688-8−8i8i0000-24ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ394ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ372−25252i5−2i52i−2i00000000−2ζ7−2ζ232ζ7+2ζ23−2ζ31−2ζ392ζ31+2ζ39−2ζ13−2ζ372ζ13+2ζ37−2ζ21−2ζ292ζ21+2ζ2900000000000000000000000000000000

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