Finite Group Databasebeta

← Group #14515020

Character table — Group #14515020

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size111122222244441212121212121212202020202424242424242424242424243030404040404040484848484848484860606080808080120120
order1222448888224455101010101010366620202020404040404040404044121224242424101010102020202048866121224
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1
χ3111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111-1-1-11
χ4111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1111-1
χ52222-2-200000000222222222222-2-2-2-20000000022-2-2000000000000-200000000
χ622-2-2-222i2i−2i−2i2-22i−2i−1+52−1−521−521+52−1+52−1−521−521+52-11-11−1+52−1−521−521+52ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ3800-11ii−i−i−1+521−521+52−1−52ζ6+ζ14−ζ6−ζ14−ζ22−ζ38ζ22+ζ380001-1i−i00
χ722-2-2-222i2i−2i−2i2-22i−2i−1−52−1+521+521−52−1−52−1+521+521−52-11-11−1−52−1+521+521−52ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ1400-11ii−i−i−1−521+521−52−1+52ζ22+ζ38−ζ22−ζ38−ζ6−ζ14ζ6+ζ140001-1i−i00
χ822-2-2-222i2i−2i−2i-22−2i2i−1+52−1−521−521+52−1+52−1−521−521+52-11-11−1+52−1−521−521+52ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ3800-11ii−i−i1−52−1+52−1−521+52−ζ6−ζ14ζ6+ζ14ζ22+ζ38−ζ22−ζ38000-11−ii00
χ922-2-2-222i2i−2i−2i-22−2i2i−1−52−1+521+521−52−1−52−1+521+521−52-11-11−1−52−1+521+521−52ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ1400-11ii−i−i1+52−1−52−1+521−52−ζ22−ζ38ζ22+ζ38ζ6+ζ14−ζ6−ζ14000-11−ii00
χ1022-2-2-22−2i−2i2i2i2-2−2i2i−1+52−1−521−521+52−1+52−1−521−521+52-11-11−1+52−1−521−521+52−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ3800-11−i−iii−1+521−521+52−1−52−ζ6−ζ14ζ6+ζ14ζ22+ζ38−ζ22−ζ380001-1−ii00
χ1122-2-2-22−2i−2i2i2i2-2−2i2i−1−52−1+521+521−52−1−52−1+521+521−52-11-11−1−52−1+521+521−52−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ1400-11−i−iii−1−521+521−52−1+52−ζ22−ζ38ζ22+ζ38ζ6+ζ14−ζ6−ζ140001-1−ii00
χ1222-2-2-22−2i−2i2i2i-222i−2i−1+52−1−521−521+52−1+52−1−521−521+52-11-11−1+52−1−521−521+52−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ3800-11−i−iii1−52−1+52−1−521+52ζ6+ζ14−ζ6−ζ14−ζ22−ζ38ζ22+ζ38000-11i−i00
χ1322-2-2-22−2i−2i2i2i-222i−2i−1−52−1+521+521−52−1−52−1+521+521−52-11-11−1−52−1+521+521−52−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ1400-11−i−iii1+52−1−52−1+521−52ζ22+ζ38−ζ22−ζ38−ζ6−ζ14ζ6+ζ14000-11i−i00
χ142-2-22002−22−2000022-2-2-2-2222-2-2200002−22−22−22−22-2002−22−20000000002−2000000
χ152-2-2200−22−22000022-2-2-2-2222-2-220000−22−22−22−222-200−22−22000000000−22000000
χ16333333333333331−521+521−521+521−521+521−521+5200001−521+521−521+521+521+521+521+521−521−521−521−52-1-10000001−521−521+521+521+521+521−521−52-1-1-10000-1-1
χ17333333333333331+521−521+521−521+521−521+521−5200001+521−521+521−521−521−521−521−521+521+521+521+52-1-10000001+521+521−521−521−521−521+521+52-1-1-10000-1-1
χ183333333333-3-3-3-31−521+521−521+521−521+521−521+5200001−521+521−521+521+521+521+521+521−521−521−521−52-1-1000000−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52-1-1-1000011
χ193333333333-3-3-3-31+521−521+521−521+521−521+521−5200001+521−521+521−521−521−521−521−521+521+521+521+52-1-1000000−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52-1-1-1000011
χ20333333-3-3-3-333-3-31−521+521−521+521−521+521−521+5200001−521+521−521+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-1-10000001−521−521+521+52−1−52−1−52−1+52−1+52-11100001-1
χ21333333-3-3-3-333-3-31+521−521+521−521+521−521+521−5200001+521−521+521−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-1-10000001+521+521−521−52−1+52−1+52−1−52−1−52-11100001-1
χ22333333-3-3-3-3-3-3331−521+521−521+521−521+521−521+5200001−521+521−521+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-1-1000000−1+52−1+52−1−52−1−521+521+521−521−52-1110000-11
χ23333333-3-3-3-3-3-3331+521−521+521−521+521−521+521−5200001+521−521+521−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-1-1000000−1−52−1−52−1+52−1+521−521−521+521+52-1110000-11
χ2444444444444444-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-100111111-1-1-1-1-1-1-1-1000111100
χ254444444444-4-4-4-4-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-10011111111111111000-1-1-1-100
χ26444444-4-4-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-1111111110011-1-1-1-1-1-1-1-1111100011-1-100
χ27444444-4-4-4-4-4-444-1-1-1-1-1-1-1-11111-1-1-1-1111111110011-1-1-1-11111-1-1-1-1000-1-11100
χ2844-4-44-400000000−1+5−1−51−51+5−1+5−1−51−51+5-22-221−51+5−1+5−1−500000000002-2000000000000000000000
χ2944-4-44-400000000−1−5−1+51+51−5−1−5−1+51+51−5-22-221+51−5−1−5−1+500000000002-2000000000000000000000
χ3044-4-4-444i4i−4i−4i4-44i−4i-1-111-1-1111-11-1-1-111ii−i−i−i−iii001-1−i−iii-111-1i−i−ii000-11−ii00
χ3144-4-4-444i4i−4i−4i-44−4i4i-1-111-1-1111-11-1-1-111ii−i−i−i−iii001-1−i−iii1-1-11−iii−i0001-1i−i00
χ3244-4-4-44−4i−4i4i4i4-4−4i4i-1-111-1-1111-11-1-1-111−i−iiiii−i−i001-1ii−i−i-111-1−iii−i000-11i−i00
χ3344-4-4-44−4i−4i4i4i-444i−4i-1-111-1-1111-11-1-1-111−i−iiiii−i−i001-1ii−i−i1-1-11i−i−ii0001-1−ii00
χ344-44-4002i2−2i2−2i22i20000−1+5−1−5−1+5−1−51−51+51−51+5-2-2220000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ370000i2−i2−i2i200000000000000000
χ354-44-4002i2−2i2−2i22i20000−1−5−1+5−1−5−1+51+51−51+51−5-2-2220000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ390000i2−i2−i2i200000000000000000
χ364-44-400−2i22i22i2−2i20000−1+5−1−5−1+5−1−51−51+51−51+5-2-2220000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ370000−i2i2i2−i200000000000000000
χ374-44-400−2i22i22i2−2i20000−1−5−1+5−1−5−1+51+51−51+51−5-2-2220000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ390000−i2i2i2−i200000000000000000
χ385555555555555500000000-1-1-1-100000000000011-1-1-1-1-1-100000000111-1-1-1-111
χ395555555555-5-5-5-500000000-1-1-1-100000000000011-1-1-1-1-1-1000000001111111-1-1
χ40555555-5-5-5-555-5-500000000-1-1-1-100000000000011-1-11111000000001-1-1-1-111-11
χ41555555-5-5-5-5-5-55500000000-1-1-1-100000000000011-1-11111000000001-1-111-1-11-1
χ426666-6-6000000001−51+51−51+51−51+51−51+50000−1+5−1−5−1+5−1−500000000-2-200000000000000200000000
χ436666-6-6000000001+51−51+51−51+51−51+51−50000−1−5−1+5−1−5−1+500000000-2-200000000000000200000000
χ4466-6-6-666i6i−6i−6i6-66i−6i11-1-111-1-1000011-1-1−i−iiiii−i−i000000001-1-11−iii−i000000000
χ4566-6-6-666i6i−6i−6i-66−6i6i11-1-111-1-1000011-1-1−i−iiiii−i−i00000000-111-1i−i−ii000000000
χ4666-6-6-66−6i−6i6i6i6-6−6i6i11-1-111-1-1000011-1-1ii−i−i−i−iii000000001-1-11i−i−ii000000000
χ4766-6-6-66−6i−6i6i6i-666i−6i11-1-111-1-1000011-1-1ii−i−i−i−iii00000000-111-1−iii−i000000000
χ486-6-660032−3232−3200001−51+5−1+5−1−5−1+5−1−51−51+500000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37-22000000000000000−22000000
χ496-6-660032−3232−3200001+51−5−1−5−1+5−1−5−1+51+51−500000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39-22000000000000000−22000000
χ506-6-6600−3232−323200001−51+5−1+5−1−5−1+5−1−51−51+500000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37-220000000000000002−2000000
χ516-6-6600−3232−323200001+51−5−1−5−1+5−1−5−1+51+51−500000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39-220000000000000002−2000000
χ528888-8-800000000-2-2-2-2-2-2-2-2222222220000000000-2-2000000000000000000000
χ5388-8-88-800000000-2-222-2-2222-22-222-2-20000000000-22000000000000000000000
χ548-88-8004i2−4i2−4i24i20000-2-2-2-2222222-2-20000i2−i2−i2i2−i2i2i2−i20000−i2i2i2−i200000000000000000
χ558-88-800−4i24i24i2−4i20000-2-2-2-2222222-2-20000−i2i2i2−i2i2−i2−i2i20000i2−i2−i2i200000000000000000
χ568-8-880042−4242−420000-2-22222-2-22-2-220000−22−22−22−2200002−22−200000000000000000
χ578-8-8800−4242−42420000-2-22222-2-22-2-2200002−22−22−22−20000−22−2200000000000000000
χ5810101010-10-100000000000000000-2-2-2-20000000000002222000000000000-200000000
χ5910-10-10100052−5252−52000000000000-222-20000000000002-200−22−220000000002−2000000
χ6010-10-101000−5252−5252000000000000-222-20000000000002-2002−22−2000000000−22000000
χ611212-12-1212-120000000022-2-222-2-20000-2-222000000000000000000000000000000000
χ6212-1212-12006i2−6i2−6i26i200002222-2-2-2-200000000−i2i2i2−i2i2−i2−i2i20000000000000000000000000
χ6312-1212-1200−6i26i26i2−6i200002222-2-2-2-200000000i2−i2−i2i2−i2i2i2−i20000000000000000000000000

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