Finite Group Databasebeta

← Group #12019675

Character table — Group #12019675

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122222444448888888888888888881010161616161616161616203232323232323232323240404040408080808080
order1225510104441010248820202020202040404040404040402244488101020204202020202020404040402448844488
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111-1-1111111111-11111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1111111-1-1-1-1-1-1-1-111-111-1-111111-1-11111-1-1-1-1111-1-1-111-1-1
χ611111111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-11111111-1-1-1-1-1-11111111-1-1-1-1-111
χ711111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-1-1-1-1111-1-111
χ811111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-111111-1-1
χ9111111111111-1-1111111111111111111-1i−ii−i-1-1-1-11-1-1ii−i−iii−i−i-1-1111-1i−ii−i
χ10111111111111-1-1111111111111111111-1−ii−ii-1-1-1-11-1-1−i−iii−i−iii-1-1111-1−ii−ii
χ11111111111111-1-11111111111111111-1-1-1i−ii−i-1-1-1-1-1-1-1ii−i−iii−i−i11-1-1-11−ii−ii
χ12111111111111-1-11111111111111111-1-1-1−ii−ii-1-1-1-1-1-1-1−i−iii−i−iii11-1-1-11i−ii−i
χ13111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111i−i−ii-1-1-1-1111ii−i−i−i−iii-1-11-1-11i−i−ii
χ14111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111−iii−i-1-1-1-1111−i−iiiii−i−i-1-11-1-11−iii−i
χ15111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11i−i−ii-1-1-1-1-111ii−i−i−i−iii11-111-1−iii−i
χ16111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11−iii−i-1-1-1-1-111−i−iiiii−i−i11-111-1i−i−ii
χ172222222-2-22222-200-2-2-2-22200000000220000022-2-2200000000002-2-20000000
χ182222222-2-22222-200-2-2-2-22200000000-2-20000022-2-2-20000000000-2220000000
χ192222222-2-2222-2200-2-2-2-222000000002200000-2-22220000000000-22-20000000
χ202222222-2-2222-2200-2-2-2-22200000000-2-200000-2-222-200000000002-220000000
χ21222−1+52−1−52−1+52−1−52222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520022222−1+52−1−52−1+52−1−520−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000000
χ22222−1+52−1−52−1+52−1−52222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002-2-2-2-2−1+52−1−52−1+52−1−520−1+52−1−521−521+521−521+521−521+521−521+520000000000
χ23222−1+52−1−52−1+52−1−52222−1+52−1−5222-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+5200-222-2-2−1+52−1−52−1+52−1−5201−521+52−1+52−1−52−1+52−1−521−521+521−521+520000000000
χ24222−1+52−1−52−1+52−1−52222−1+52−1−5222-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+5200-2-2-222−1+52−1−52−1+52−1−5201−521+521−521+521−521+52−1+52−1−52−1+52−1−520000000000
χ25222−1+52−1−52−1+52−1−52222−1+52−1−52-2-222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-22i−2i2i−2i1−521+521−521+5201−521+52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ26222−1+52−1−52−1+52−1−52222−1+52−1−52-2-222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2−2i2i−2i2i1−521+521−521+5201−521+52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ27222−1+52−1−52−1+52−1−52222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+520022i−2i−2i2i1−521+521−521+520−1+52−1−52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ28222−1+52−1−52−1+52−1−52222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52002−2i2i2i−2i1−521+521−521+520−1+52−1−52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ29222−1−52−1+52−1−52−1+52222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520022222−1−52−1+52−1−52−1+520−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000000
χ30222−1−52−1+52−1−52−1+52222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52002-2-2-2-2−1−52−1+52−1−52−1+520−1−52−1+521+521−521+521−521+521−521+521−520000000000
χ31222−1−52−1+52−1−52−1+52222−1−52−1+5222-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200-222-2-2−1−52−1+52−1−52−1+5201+521−52−1−52−1+52−1−52−1+521+521−521+521−520000000000
χ32222−1−52−1+52−1−52−1+52222−1−52−1+5222-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200-2-2-222−1−52−1+52−1−52−1+5201+521−521+521−521+521−52−1−52−1+52−1−52−1+520000000000
χ33222−1−52−1+52−1−52−1+52222−1−52−1+52-2-222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-22i−2i2i−2i1+521−521+521−5201+521−52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
χ34222−1−52−1+52−1−52−1+52222−1−52−1+52-2-222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2−2i2i−2i2i1+521−521+521−5201+521−52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
χ35222−1−52−1+52−1−52−1+52222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−520022i−2i−2i2i1+521−521+521−520−1−52−1+52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
χ36222−1−52−1+52−1−52−1+52222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52002−2i2i2i−2i1+521−521+521−520−1−52−1+52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
χ37444444400-44400000000-4-40000000044000000000-400000000000000000000
χ38444444400-44400000000-4-400000000-4-4000000000400000000000000000000
χ39444−1+5−1−5−1+5−1−5-4-44−1+5−1−54-4001−51−51+51+5−1+5−1−5000000000000000−1+5−1−51−51+5000000000000000000000
χ40444−1+5−1−5−1+5−1−5-4-44−1+5−1−5-44001−51−51+51+5−1+5−1−50000000000000001−51+5−1+5−1−5000000000000000000000
χ41444−1−5−1+5−1−5−1+5-4-44−1−5−1+54-4001+51+51−51−5−1−5−1+5000000000000000−1−5−1+51+51−5000000000000000000000
χ42444−1−5−1+5−1−5−1+5-4-44−1−5−1+5-44001+51+51−51−5−1−5−1+50000000000000001+51−5−1−5−1+5000000000000000000000
χ4344-44444000-4-4002i−2i0000002i2i−2i−2i2i2i−2i−2i4-4000000000000000000000002i−2i00000
χ4444-44444000-4-4002i−2i0000002i2i−2i−2i2i2i−2i−2i-4400000000000000000000000−2i2i00000
χ4544-44444000-4-400−2i2i000000−2i−2i2i2i−2i−2i2i2i4-400000000000000000000000−2i2i00000
χ4644-44444000-4-400−2i2i000000−2i−2i2i2i−2i−2i2i2i-44000000000000000000000002i−2i00000
χ47888−2+25−2−25−2+25−2−2500-8−2+25−2−25000000002−252+250000000000000000000000000000000000000000
χ48888−2−25−2+25−2−25−2+2500-8−2−25−2+25000000002+252−250000000000000000000000000000000000000000
χ4988-8−2+25−2−25−2+25−2−250002−252+25004i−4i000000−2ζ22−2ζ38−2ζ22−2ζ382ζ22+2ζ382ζ22+2ζ38−2ζ6−2ζ14−2ζ6−2ζ142ζ6+2ζ142ζ6+2ζ1400000000000000000000000000000000
χ5088-8−2+25−2−25−2+25−2−250002−252+2500−4i4i0000002ζ22+2ζ382ζ22+2ζ38−2ζ22−2ζ38−2ζ22−2ζ382ζ6+2ζ142ζ6+2ζ14−2ζ6−2ζ14−2ζ6−2ζ1400000000000000000000000000000000
χ5188-8−2−25−2+25−2−25−2+250002+252−25004i−4i000000−2ζ6−2ζ14−2ζ6−2ζ142ζ6+2ζ142ζ6+2ζ14−2ζ22−2ζ38−2ζ22−2ζ382ζ22+2ζ382ζ22+2ζ3800000000000000000000000000000000
χ5288-8−2−25−2+25−2−25−2+250002+252−2500−4i4i0000002ζ6+2ζ142ζ6+2ζ14−2ζ6−2ζ14−2ζ6−2ζ142ζ22+2ζ382ζ22+2ζ38−2ζ22−2ζ38−2ζ22−2ζ3800000000000000000000000000000000
χ538-8088-8-84i−4i00000004i−4i4i−4i000000000000000000000000000000000000000000
χ548-8088-8-8−4i4i0000000−4i4i−4i4i000000000000000000000000000000000000000000
χ558-80−2+25−2−252−252+254i−4i0000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14002ζ7−2ζ23−2ζ7+2ζ23−2ζ13+2ζ372ζ13−2ζ37−2ζ31+2ζ392ζ31−2ζ39−2ζ21+2ζ292ζ21−2ζ2900000000000000000000000000000000
χ568-80−2+25−2−252−252+254i−4i0000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400−2ζ7+2ζ232ζ7−2ζ232ζ13−2ζ37−2ζ13+2ζ372ζ31−2ζ39−2ζ31+2ζ392ζ21−2ζ29−2ζ21+2ζ2900000000000000000000000000000000
χ578-80−2+25−2−252−252+25−4i4i00000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400−2ζ13+2ζ372ζ13−2ζ372ζ7−2ζ23−2ζ7+2ζ23−2ζ21+2ζ292ζ21−2ζ29−2ζ31+2ζ392ζ31−2ζ3900000000000000000000000000000000
χ588-80−2+25−2−252−252+25−4i4i00000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14002ζ13−2ζ37−2ζ13+2ζ37−2ζ7+2ζ232ζ7−2ζ232ζ21−2ζ29−2ζ21+2ζ292ζ31−2ζ39−2ζ31+2ζ3900000000000000000000000000000000
χ598-80−2−25−2+252+252−254i−4i0000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800−2ζ31+2ζ392ζ31−2ζ39−2ζ21+2ζ292ζ21−2ζ29−2ζ7+2ζ232ζ7−2ζ232ζ13−2ζ37−2ζ13+2ζ3700000000000000000000000000000000
χ608-80−2−25−2+252+252−254i−4i0000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38002ζ31−2ζ39−2ζ31+2ζ392ζ21−2ζ29−2ζ21+2ζ292ζ7−2ζ23−2ζ7+2ζ23−2ζ13+2ζ372ζ13−2ζ3700000000000000000000000000000000
χ618-80−2−25−2+252+252−25−4i4i00000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800−2ζ21+2ζ292ζ21−2ζ29−2ζ31+2ζ392ζ31−2ζ392ζ13−2ζ37−2ζ13+2ζ37−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000000000
χ628-80−2−25−2+252+252−25−4i4i00000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38002ζ21−2ζ29−2ζ21+2ζ292ζ31−2ζ39−2ζ31+2ζ39−2ζ13+2ζ372ζ13−2ζ372ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000000000

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