Finite Group Databasebeta

← Group #13026419

Character table — Group #13026419

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111122222244444444444444444444888888888888888888888888888820202020202020202020202040408080808080808080
order12442488882458810101020202020404040404040404044881010202020202020202020204040404040404040404040402222444488888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1ii−i−i−i−iii
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1−i−iiiii−i−i
χ7111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111
χ9111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-11-11-11-1
χ10111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-11-11-11
χ11111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111i−i−iii−i−ii
χ12111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−iii−i−iii−i
χ13111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111i−i−ii−iii−i
χ14111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111−iii−ii−i−ii
χ15111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-11-11-1-11-11
χ16111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-11-111-11-1
χ172222222222-2-22-2-22222222222222220000-2-2-2-200000000-2-2-2-200000000002-200-2200002-200000000
χ182222222222-2-22-2-22222222222222220000-2-2-2-200000000-2-2-2-20000000000-22002-20000-2200000000
χ19222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000-2-2-2-200000000222200000000002-200-220000-2200000000
χ20222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000-2-2-2-20000000022220000000000-22002-200002-200000000
χ2122-2-22-200002-2200222-2-2-2-2000000002-20022-2-22222-2-2-2-2000000000000222-2-2-22-200000000000000
χ2222-2-22-200002-2200222-2-2-2-2000000002-20022-2-22222-2-2-2-2000000000000-2-2-2222-2200000000000000
χ2322-2-22-200002-2200222-2-2-2-200000000-220022-2-2-2-2-2-2222200000000000022-22-2-2-2200000000000000
χ2422-2-22-200002-2200222-2-2-2-200000000-220022-2-2-2-2-2-22222000000000000-2-22-2222-200000000000000
χ2522-2-22-20000-22200222-2-2-2-200000000002i−2i-2-2220000000000002i2i2i2i−2i−2i−2i−2i002200-2-22i2i−2i−2i0000000000
χ2622-2-22-20000-22200222-2-2-2-200000000002i−2i-2-2220000000000002i2i2i2i−2i−2i−2i−2i00-2-20022−2i−2i2i2i0000000000
χ2722-2-22-20000-22200222-2-2-2-20000000000−2i2i-2-222000000000000−2i−2i−2i−2i2i2i2i2i002200-2-2−2i−2i2i2i0000000000
χ2822-2-22-20000-22200222-2-2-2-20000000000−2i2i-2-222000000000000−2i−2i−2i−2i2i2i2i2i00-2-200222i2i−2i−2i0000000000
χ29444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ30444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-111111111-1-1-1-1111111110000000000000000000000
χ314444444444-4-4-1-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000111155−5−555−5−5111155−5−555−5−50000000000000000000000
χ324444444444-4-4-1-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111−5−555−5−5551111−5−555−5−5550000000000000000000000
χ33444444-4-4-4-444-1-4-4-1-1-1-1-1-1-11111111144-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000
χ34444444-4-4-4-444-1-4-4-1-1-1-1-1-1-111111111-4-444-1-1-1-1111111111111-1-1-1-1-1-1-1-10000000000000000000000
χ35444444-4-4-4-4-4-4-144-1-1-1-1-1-1-1111111110000111155−5−555−5−5-1-1-1-1−5−555−5−5550000000000000000000000
χ36444444-4-4-4-4-4-4-144-1-1-1-1-1-1-11111111100001111−5−555−5−555-1-1-1-155−5−555−5−50000000000000000000000
χ374444-4-400000044i−4i4-4-444-4-40000000000000000000000004i4i−4i−4i000000000000000000000000000000
χ384444-4-40000004−4i4i4-4-444-4-4000000000000000000000000−4i−4i4i4i000000000000000000000000000000
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χ404444-4-4000000-14i−4i-111-1-111i5i5i5i5−i5−i5−i5−i500005−55−5ζ6−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+ζ38−i−iiiζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000000000000
χ414444-4-4000000-14i−4i-111-1-111−i5−i5−i5−i5i5i5i5i50000−55−55ζ6−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+ζ38−i−iii−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000000000000
χ424444-4-4000000-14i−4i-111-1-111−i5−i5−i5−i5i5i5i5i50000−55−55−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−ζ38−i−iiiζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ360000000000000000000000
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χ444444-4-4000000-1−4i4i-111-1-111i5i5i5i5−i5−i5−i5−i50000−55−55−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−ζ38ii−i−i−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000000000000
χ454444-4-4000000-1−4i4i-111-1-111−i5−i5−i5−i5i5i5i5i500005−55−5−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−ζ38ii−i−iζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000000000000
χ464444-4-4000000-1−4i4i-111-1-111−i5−i5−i5−i5i5i5i5i500005−55−5ζ6−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+ζ38ii−i−i−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ360000000000000000000000
χ4744-4-44-400004-4-100-1-1-11111i5i5−i5−i5i5i5−i5−i54-400-1-111-1-1-1-11111i5−i5i5−i5i5i5−i5−i5−i5−i5i5i50000000000000000000000
χ4844-4-44-400004-4-100-1-1-11111i5i5−i5−i5i5i5−i5−i5-4400-1-1111111-1-1-1-1i5−i5i5−i5−i5−i5i5i5i5i5−i5−i50000000000000000000000
χ4944-4-44-400004-4-100-1-1-11111−i5−i5i5i5−i5−i5i5i54-400-1-111-1-1-1-11111−i5i5−i5i5−i5−i5i5i5i5i5−i5−i50000000000000000000000
χ5044-4-44-400004-4-100-1-1-11111−i5−i5i5i5−i5−i5i5i5-4400-1-1111111-1-1-1-1−i5i5−i5i5i5i5−i5−i5−i5−i5i5i50000000000000000000000
χ5144-4-44-40000-44-100-1-1-11111i5i5−i5−i5i5i5−i5−i5004i−4i11-1-155−5−5−5−555−i5i5−i5i5−i−i−i−iiiii0000000000000000000000
χ5244-4-44-40000-44-100-1-1-11111i5i5−i5−i5i5i5−i5−i500−4i4i11-1-1−5−55555−5−5−i5i5−i5i5iiii−i−i−i−i0000000000000000000000
χ5344-4-44-40000-44-100-1-1-11111−i5−i5i5i5−i5−i5i5i5004i−4i11-1-1−5−55555−5−5i5−i5i5−i5−i−i−i−iiiii0000000000000000000000
χ5444-4-44-40000-44-100-1-1-11111−i5−i5i5i5−i5−i5i5i500−4i4i11-1-155−5−5−5−555i5−i5i5−i5iiii−i−i−i−i0000000000000000000000
χ5544-4-4-4444-4-4004004-4-4-4-44444-4-4-4-44400000000000000000000000000000000000000000000000000
χ5644-4-4-4444-4-400-100-11111-1-1-1-11111-1-100005−5−55−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+ζ385−5−55ζ6−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
χ5744-4-4-4444-4-400-100-11111-1-1-1-11111-1-100005−5−55ζ6−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−ζ385−5−55−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
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χ654-44i−4i002i2−2i222−2200400-4004i−4i002i2−2i222−2222−222i2−2i200000000000000000000000000002-2002i−2i00−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ664-44i−4i002i2−2i222−2200400-4004i−4i002i2−2i222−2222−222i2−2i20000000000000000000000000000-2200−2i2i002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ674-44i−4i00−2i22i2−222200400-4004i−4i00−2i22i2−2222−2222−2i22i200000000000000000000000000002-2002i−2i002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ684-44i−4i00−2i22i2−222200400-4004i−4i00−2i22i2−2222−2222−2i22i20000000000000000000000000000-2200−2i2i00−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ694-4−4i4i002i2−2i2−222200400-400−4i4i002i2−2i2−2222−22222i2−2i200000000000000000000000000002-200−2i2i00−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ704-4−4i4i002i2−2i2−222200400-400−4i4i002i2−2i2−2222−22222i2−2i20000000000000000000000000000-22002i−2i002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ714-4−4i4i00−2i22i222−2200400-400−4i4i00−2i22i222−2222−22−2i22i200000000000000000000000000002-200−2i2i002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ724-4−4i4i00−2i22i222−2200400-400−4i4i00−2i22i222−2222−22−2i22i20000000000000000000000000000-22002i−2i00−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ738-88i−8i004i2−4i242−4200-200225−25−2i2i2i5−2i52ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ39−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ292ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ3900000000000000000000000000000000000000000000000000
χ748-88i−8i004i2−4i242−4200-2002−2525−2i2i−2i52i52ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ39−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ292ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ392ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ2900000000000000000000000000000000000000000000000000
χ758-88i−8i00−4i24i2−424200-200225−25−2i2i2i5−2i5−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ392ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ3900000000000000000000000000000000000000000000000000
χ768-88i−8i00−4i24i2−424200-2002−2525−2i2i−2i52i5−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ392ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ29−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ2900000000000000000000000000000000000000000000000000
χ778-8−8i8i004i2−4i2−424200-200225−252i−2i−2i52i52ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ29−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ392ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ2900000000000000000000000000000000000000000000000000
χ788-8−8i8i004i2−4i2−424200-2002−25252i−2i2i5−2i52ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ29−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ392ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ292ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ3900000000000000000000000000000000000000000000000000
χ798-8−8i8i00−4i24i242−4200-200225−252i−2i−2i52i5−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ292ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ2900000000000000000000000000000000000000000000000000
χ808-8−8i8i00−4i24i242−4200-2002−25252i−2i2i5−2i5−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ292ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ39−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ3900000000000000000000000000000000000000000000000000

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