Finite Group Databasebeta

← Group #13024809

Character table — Group #13024809

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222444444448888888101016161616161616161616161616162020202020404040404040404040808080808080
order12244244451010104202020202020882410101010102020202020202088888816161616161616162416161616
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111-1-11-1-1-1-1111-1-1-1-111111111111111-1-1-1-1-1-1
χ41111111111111111111111-1-11-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ611111111111111111111-1-111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ711111111111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ911111-1-1-1-11111111-1-1-1-1111-1-11111-111-1-1-1-11-1-1-1-11ii−i−iii−i−i1-1i−ii−i
χ1011111-1-1-1-11111111-1-1-1-1111-1-11111-111-1-1-1-11-1-1-1-11−i−iii−i−iii1-1−ii−ii
χ1111111-1-1-1-11111111-1-1-1-111-11-1-1-1-1-1-11111111-1-1-1-11ii−i−iii−i−i-11−ii−ii
χ1211111-1-1-1-11111111-1-1-1-111-11-1-1-1-1-1-11111111-1-1-1-11−i−iii−i−iii-11i−ii−i
χ1311111-1-1-1-11111111-1-1-1-1-1-11-1-11111-111-1-1-1-1-11111-111-1-1-1-111-111-1-11
χ1411111-1-1-1-11111111-1-1-1-1-1-11-1-11111-111-1-1-1-1-11111-1-1-11111-1-1-11-111-1
χ1511111-1-1-1-11111111-1-1-1-1-1-1-11-1-1-1-1-1-1111111-11111-111-1-1-1-1111-1-111-1
χ1611111-1-1-1-11111111-1-1-1-1-1-1-11-1-1-1-1-1-1111111-11111-1-1-11111-1-11-11-1-11
χ172222222-2-22222-222-2-2-2-22200200002-2-20000222-2-2-200000000000000
χ182222222-2-22222-222-2-2-2-2-2-200200002-2-20000-2-2-222200000000000000
χ1922222-2-2222222-22222222200-20000-2-2-200002-2-222-200000000000000
χ2022222-2-2222222-2222222-2-200-20000-2-2-20000-222-2-2200000000000000
χ2122-22-2002i−2i22-2-202-22i2i−2i−2i2200000000000000-2002i−2i01+i−1−i1−i−1+i1+i−1−i1−i−1+i000000
χ2222-22-2002i−2i22-2-202-22i2i−2i−2i2200000000000000-2002i−2i0−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000
χ2322-22-2002i−2i22-2-202-22i2i−2i−2i-2-200000000000000200−2i2i01−i−1+i−1−i1+i−1+i1−i1+i−1−i000000
χ2422-22-2002i−2i22-2-202-22i2i−2i−2i-2-200000000000000200−2i2i0−1+i1−i1+i−1−i1−i−1+i−1−i1+i000000
χ2522-22-200−2i2i22-2-202-2−2i−2i2i2i2200000000000000-200−2i2i01−i−1+i1+i−1−i1−i−1+i1+i−1−i000000
χ2622-22-200−2i2i22-2-202-2−2i−2i2i2i2200000000000000-200−2i2i0−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000
χ2722-22-200−2i2i22-2-202-2−2i−2i2i2i-2-2000000000000002002i−2i01+i−1−i−1+i1−i−1−i1+i1−i−1+i000000
χ2822-22-200−2i2i22-2-202-2−2i−2i2i2i-2-2000000000000002002i−2i0−1−i1+i1−i−1+i1+i−1−i−1+i1−i000000
χ29444444444-1-1-1-14-1-1-1-1-1-10044-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ30444444444-1-1-1-14-1-1-1-1-1-100-4-4-11111-1-1-1111100000000000000000000
χ314444444-4-4-1-1-1-1-4-1-111110000-155−5−5-11155−5−500000000000000000000
χ324444444-4-4-1-1-1-1-4-1-111110000-1−5−555-111−5−55500000000000000000000
χ3344444-4-444-1-1-1-1-4-1-1-1-1-1-10000155−5−5111−5−55500000000000000000000
χ3444444-4-444-1-1-1-1-4-1-1-1-1-1-100001−5−55511155−5−500000000000000000000
χ3544444-4-4-4-4-1-1-1-14-1-11111004-41-1-1-1-11-1-1111100000000000000000000
χ3644444-4-4-4-4-1-1-1-14-1-1111100-44111111-1-1-1-1-1-100000000000000000000
χ37444-4-44-40044440-4-40000000040000-400000000000000000000000000
χ38444-4-44-400-1-1-1-10115−55−50000-1−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3615−5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000
χ39444-4-44-400-1-1-1-10115−55−50000-1ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3615−5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000
χ40444-4-44-400-1-1-1-1011−55−550000-1−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ361−55−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000
χ41444-4-44-400-1-1-1-1011−55−550000-1ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ361−55ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000
χ42444-4-4-440044440-4-400000000-40000400000000000000000000000000
χ43444-4-4-4400-1-1-1-10115−55−500001−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36-1−55ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000
χ44444-4-4-4400-1-1-1-10115−55−500001ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36-1−55−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000
χ45444-4-4-4400-1-1-1-1011−55−5500001−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36-15−5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000
χ46444-4-4-4400-1-1-1-1011−55−5500001ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36-15−5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000
χ4744-4-44000044-4-40-440000000000000000000004i−4i00000000000000000
χ4844-4-44000044-4-40-44000000000000000000000−4i4i00000000000000000
χ4988-88-8008i−8i-2-2220-22−2i−2i2i2i000000000000000000000000000000000000
χ5088-88-800−8i8i-2-2220-222i2i−2i−2i000000000000000000000000000000000000
χ5188-8-880000-2-22202-22i5−2i5−2i52i5000000000000000000000000000000000000
χ5288-8-880000-2-22202-2−2i52i52i5−2i5000000000000000000000000000000000000
χ538-800000008-800000000042−420000000000000000000000000000000000
χ548-800000008-8000000000−42420000000000000000000000000000000000
χ5516-160000000-4445−450000000000000000000000000000000000000000000
χ5616-160000000-44−45450000000000000000000000000000000000000000000

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