Finite Group Databasebeta

← Group #13026440

Character table — Group #13026440

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444488888888888888888816161616161616162020202020202020404040408080808080808080
order12442424510101020202020248888101020204040404040404040101020204040404022448888448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iii
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i
χ91111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-11-11-11-1
χ101111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-11-11-11
χ111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1i−ii−i−ii−ii
χ121111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−ii−iii−ii−i
χ131111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-111-1-11
χ141111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-111-1
χ151111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111i−i−ii−iii−i
χ161111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−iii−ii−i−ii
χ17222222-2-22222222200002-2-2-2-2-200000000000022-2-22-22-222-2-2000000000000
χ18222222-2-22222222200002-2-2-2-2-200000000000022-2-2-22-22-2-222000000000000
χ19222222-2-2222222220000-22-2-2-2-2000000000000-2-2222-22-2-2-222000000000000
χ20222222-2-2222222220000-22-2-2-2-2000000000000-2-222-22-2222-2-2000000000000
χ2122-2-22-22-22222-2-2-2-2002i−2i0022-2-22i2i2i2i−2i−2i−2i−2i000000002-2-220000002i−2i00000000
χ2222-2-22-22-22222-2-2-2-2002i−2i0022-2-22i2i2i2i−2i−2i−2i−2i00000000-222-2000000−2i2i00000000
χ2322-2-22-22-22222-2-2-2-200−2i2i0022-2-2−2i−2i−2i−2i2i2i2i2i000000002-2-22000000−2i2i00000000
χ2422-2-22-22-22222-2-2-2-200−2i2i0022-2-2−2i−2i−2i−2i2i2i2i2i00000000-222-20000002i−2i00000000
χ2522-2-22-2-222222-2-2-2-22-20000-2-2220000000022-2-2000022-2-200002-20000000000
χ2622-2-22-2-222222-2-2-2-22-20000-2-2220000000022-2-20000-2-2220000-220000000000
χ2722-2-22-2-222222-2-2-2-2-220000-2-22200000000-2-222000022-2-20000-220000000000
χ2822-2-22-2-222222-2-2-2-2-220000-2-22200000000-2-2220000-2-22200002-20000000000
χ2944444444-1-1-1-1-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ3044444444-1-1-1-1-1-1-1-144-4-4-4-4-1-1-1-111111111-1-1-1-1111100000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-444-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-1111111111111-1-1-1-100000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-100004-4111155−5−555−5−55−55−5-1-11100000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-100004-41111−5−555−5−555−55−55-1-11100000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-10000-44111155−5−555−5−5−55−5511-1-100000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-10000-441111−5−555−5−5555−55−511-1-100000000000000000000
χ374444-4-4004-4-4444-4-4000000000000000000000000000000004i−4i000000000000
χ384444-4-4004-4-4444-4-400000000000000000000000000000000−4i4i000000000000
χ3944-4-44-44-4-1-1-1-11111004i−4i00-1-111−i−i−i−iiiii5−5−55i5−i5i5−i500000000000000000000
χ4044-4-44-44-4-1-1-1-11111004i−4i00-1-111−i−i−i−iiiii−555−5−i5i5−i5i500000000000000000000
χ4144-4-44-44-4-1-1-1-1111100−4i4i00-1-111iiii−i−i−i−i5−5−55−i5i5−i5i500000000000000000000
χ4244-4-44-44-4-1-1-1-1111100−4i4i00-1-111iiii−i−i−i−i−555−5i5−i5i5−i500000000000000000000
χ4344-4-44-4-44-1-1-1-111114-4000011-1-1i5i5−i5−i5−i5−i5i5i5-1-111i5−i5−i5i500000000000000000000
χ4444-4-44-4-44-1-1-1-111114-4000011-1-1−i5−i5i5i5i5i5−i5−i5-1-111−i5i5i5−i500000000000000000000
χ4544-4-44-4-44-1-1-1-11111-44000011-1-1i5i5−i5−i5−i5−i5i5i511-1-1−i5i5i5−i500000000000000000000
χ4644-4-44-4-44-1-1-1-11111-44000011-1-1−i5−i5i5i5i5i5−i5−i511-1-1i5−i5−i5i500000000000000000000
χ4744-4-4-44004-4-44-4-4440000000000000000000000000000004-400000000000000
χ4844-4-4-44004-4-44-4-444000000000000000000000000000000-4400000000000000
χ498888-8-800-222-2-2-22200000025−2525−25000000000000000000000000000000000000
χ508888-8-800-222-2-2-222000000−2525−2525000000000000000000000000000000000000
χ5188-8-8-8800-222-222-2-200000025−25−2525000000000000000000000000000000000000
χ5288-8-8-8800-222-222-2-2000000−252525−25000000000000000000000000000000000000
χ538-88i−8i0000800-88i−8i000000000000000000000000000000000000000000000000
χ548-88i−8i0000-225−252−2i2i2i5−2i50000000000−2ζ21+2ζ292ζ21−2ζ29−2ζ13+2ζ372ζ13−2ζ37−2ζ31+2ζ392ζ31−2ζ392ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000
χ558-88i−8i0000-225−252−2i2i2i5−2i500000000002ζ21−2ζ29−2ζ21+2ζ292ζ13−2ζ37−2ζ13+2ζ372ζ31−2ζ39−2ζ31+2ζ39−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000
χ568-88i−8i0000-2−25252−2i2i−2i52i50000000000−2ζ13+2ζ372ζ13−2ζ372ζ21−2ζ29−2ζ21+2ζ292ζ7−2ζ23−2ζ7+2ζ232ζ31−2ζ39−2ζ31+2ζ390000000000000000000000000000
χ578-88i−8i0000-2−25252−2i2i−2i52i500000000002ζ13−2ζ37−2ζ13+2ζ37−2ζ21+2ζ292ζ21−2ζ29−2ζ7+2ζ232ζ7−2ζ23−2ζ31+2ζ392ζ31−2ζ390000000000000000000000000000
χ588-8−8i8i0000800-8−8i8i000000000000000000000000000000000000000000000000
χ598-8−8i8i0000-225−2522i−2i−2i52i50000000000−2ζ31+2ζ392ζ31−2ζ392ζ7−2ζ23−2ζ7+2ζ23−2ζ21+2ζ292ζ21−2ζ29−2ζ13+2ζ372ζ13−2ζ370000000000000000000000000000
χ608-8−8i8i0000-225−2522i−2i−2i52i500000000002ζ31−2ζ39−2ζ31+2ζ39−2ζ7+2ζ232ζ7−2ζ232ζ21−2ζ29−2ζ21+2ζ292ζ13−2ζ37−2ζ13+2ζ370000000000000000000000000000
χ618-8−8i8i0000-2−252522i−2i2i5−2i500000000002ζ7−2ζ23−2ζ7+2ζ232ζ31−2ζ39−2ζ31+2ζ39−2ζ13+2ζ372ζ13−2ζ372ζ21−2ζ29−2ζ21+2ζ290000000000000000000000000000
χ628-8−8i8i0000-2−252522i−2i2i5−2i50000000000−2ζ7+2ζ232ζ7−2ζ23−2ζ31+2ζ392ζ31−2ζ392ζ13−2ζ37−2ζ13+2ζ37−2ζ21+2ζ292ζ21−2ζ290000000000000000000000000000

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