Finite Group Databasebeta

← Group #13015105

Character table — Group #13015105

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111114444444444444488888888888810101010101010101616161616161616161620202020404040404040404040404040404040408080
order12222222444444510101010101010202020202020202020202020444444444420202020202020204444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11-1
χ101111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111-1
χ111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-11
χ121111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-11-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1-11
χ131111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-11
χ141111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-11
χ151111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−i1-1
χ161111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iii1-1
χ1722222222-2-222-2-222222222-2-2-2-22222-2-2-2-222-2-222-2-2000000000022-2-2000000000000000000
χ1822222222-2-222-2-222222222-2-2-2-22222-2-2-2-2-2-222-2-2220000000000-2-222000000000000000000
χ1922222222-2-2-2-22222222222-2-2-2-2-2-2-2-2222222-2-222-2-20000000000-2-222000000000000000000
χ2022222222-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-222-2-222000000000022-2-2000000000000000000
χ2122-2-222-2-22-200002-2-22-2-22222-2-2000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
χ2222-2-222-2-22-200002-2-22-2-22222-2-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900
χ2322-2-222-2-22-200002-2-22-2-22222-2-200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
χ2422-2-222-2-22-200002-2-22-2-22222-2-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700
χ2522-2-222-2-2-2200002-2-22-2-222-2-222000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ2622-2-222-2-2-2200002-2-22-2-222-2-222000000002i−2i−2i2i2i−2i−2i2i00000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ2722-2-222-2-2-2200002-2-22-2-222-2-22200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ2822-2-222-2-2-2200002-2-22-2-222-2-22200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ292-22-22-22-200002i−2i22-2-22-22-2000000002i2i−2i−2i002i−2i00−2i2i00000000002-2001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000
χ302-22-22-22-200002i−2i22-2-22-22-2000000002i2i−2i−2i002i−2i00−2i2i00000000002-200−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000
χ312-22-22-22-200002i−2i22-2-22-22-2000000002i2i−2i−2i00−2i2i002i−2i0000000000-22001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000
χ322-22-22-22-200002i−2i22-2-22-22-2000000002i2i−2i−2i00−2i2i002i−2i0000000000-2200−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000
χ332-22-22-22-20000−2i2i22-2-22-22-200000000−2i−2i2i2i002i−2i00−2i2i0000000000-22001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000
χ342-22-22-22-20000−2i2i22-2-22-22-200000000−2i−2i2i2i002i−2i00−2i2i0000000000-2200−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000
χ352-22-22-22-20000−2i2i22-2-22-22-200000000−2i−2i2i2i00−2i2i002i−2i00000000002-2001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000
χ362-22-22-22-20000−2i2i22-2-22-22-200000000−2i−2i2i2i00−2i2i002i−2i00000000002-200−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000
χ3744444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000044-1-1-1-1-1-1-1-10000000000000000000000
χ3844444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-4-4111111110000000000000000000000
χ394444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-111111111000000004-4-1-1-1-111110000000000000000000000
χ404444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000-441111-1-1-1-10000000000000000000000
χ4144444444-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-11111000000000055−5−555−5−50000000000000000000000
χ4244444444-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-111110000000000−5−555−5−5550000000000000000000000
χ4344444444-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-1000000000055−5−5−5−5550000000000000000000000
χ4444444444-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-10000000000−5−55555−5−50000000000000000000000
χ454444-4-4-4-4004-4004-4-4444-4-4000044-4-400000000000000000000000000000000000000000000
χ464444-4-4-4-4004-400-111-1-1-1115−55−5-1-1115−55−50000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000
χ474444-4-4-4-4004-400-111-1-1-1115−55−5-1-1115−55−50000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000
χ484444-4-4-4-4004-400-111-1-1-111−55−55-1-111−55−550000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000
χ494444-4-4-4-4004-400-111-1-1-111−55−55-1-111−55−550000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000
χ504444-4-4-4-400-44004-4-4444-4-40000-4-44400000000000000000000000000000000000000000000
χ514444-4-4-4-400-4400-111-1-1-1115−55−511-1-1−55−550000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000
χ524444-4-4-4-400-4400-111-1-1-1115−55−511-1-1−55−550000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000
χ534444-4-4-4-400-4400-111-1-1-111−55−5511-1-15−55−50000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000
χ544444-4-4-4-400-4400-111-1-1-111−55−5511-1-15−55−50000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000
χ5544-4-4-4-4440000004444-4-4-4-4000000000000000000000000000000004i−4i000000000000000000
χ5644-4-4-4-4440000004444-4-4-4-400000000000000000000000000000000−4i4i000000000000000000
χ574-44-4-44-440000004-44-44-4-440000000000004i−4i00−4i4i0000000000000000000000000000000000
χ584-44-4-44-440000004-44-44-4-44000000000000−4i4i004i−4i0000000000000000000000000000000000
χ594-4-444-4-440000004-44-4-444-4000000000000004400-4-400000000000000000000000000000000
χ604-4-444-4-440000004-44-4-444-400000000000000-4-4004400000000000000000000000000000000
χ614-4-44-444-400000044-4-4-44-440000000000004400-4-40000000000000000000000000000000000
χ624-4-44-444-400000044-4-4-44-44000000000000-4-400440000000000000000000000000000000000
χ6388-8-888-8-88-80000-222-222-2-2-2-222000000000000000000000000000000000000000000000000
χ6488-8-888-8-8-880000-222-222-2-222-2-2000000000000000000000000000000000000000000000000
χ6588-8-8-8-888000000-2-2-2-2222225−25−2525000000000000000000000000000000000000000000000000
χ6688-8-8-8-888000000-2-2-2-22222−252525−25000000000000000000000000000000000000000000000000
χ678-88-88-88-800008i−8i-2-222-22-2200000000−2i−2i2i2i0000000000000000000000000000000000000000
χ688-88-88-88-80000−8i8i-2-222-22-22000000002i2i−2i−2i0000000000000000000000000000000000000000
χ698-88-8-88-88000000-22-22-222-2000000002i5−2i5−2i52i50000000000000000000000000000000000000000
χ708-88-8-88-88000000-22-22-222-200000000−2i52i52i5−2i50000000000000000000000000000000000000000
χ718-8-888-8-88000000-22-222-2-2200002i5−2i52i5−2i500000000000000000000000000000000000000000000
χ728-8-888-8-88000000-22-222-2-220000−2i52i5−2i52i500000000000000000000000000000000000000000000
χ738-8-88-888-8000000-2-2222-22-200002i5−2i5−2i52i500000000000000000000000000000000000000000000
χ748-8-88-888-8000000-2-2222-22-20000−2i52i52i5−2i500000000000000000000000000000000000000000000

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