Finite Group Databasebeta

← Group #13027364

Character table — Group #13027364

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222444444448888888101016161616161616161616161616162020202020404040404040404040808080808080
order12244245881010108101020202020882410101010202020204040404022448444488888248888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-11111
χ511111111111111111111-1-111111111111111-1-1-1-1-1ii−i−i-1ii−i−i-1-1ii−i−i
χ611111111111111111111-1-111111111111111-1-1-1-1-1−i−iii-1−i−iii-1-1−i−iii
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1ii−i−i-1ii−i−i11−i−iii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1−i−iii-1−i−iii11ii−i−i
χ911111111-1-1111-1111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11ii−i−i1−i−iii1-1i−ii−i
χ1011111111-1-1111-1111111111-11111-1-1-1-1-1-1-1-1-1-1-1-11−i−iii1ii−i−i1-1−ii−ii
χ1111111111-1-1111-111111111-11-1-1-1-11111-1-1-1-1-1-1-1-11ii−i−i1−i−iii-11−ii−ii
χ1211111111-1-1111-111111111-11-1-1-1-11111-1-1-1-1-1-1-1-11−i−iii1ii−i−i-11i−ii−i
χ1311111111-1-1111-1111111-1-11-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-111-1-11
χ1411111111-1-1111-1111111-1-11-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-111-1
χ1511111111-1-1111-1111111-1-1-11-1-1-1-11111-1-1-1-11111-11111-1-1-1-1-11-1-111-1
χ1611111111-1-1111-1111111-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111-11-1-11
χ1722222-2-2222222-2-2-22-2-2222000000000022-2-2-222-220000-20000000000
χ1822222-2-2222222-2-2-22-2-22-2-2000000000022-2-22-2-22-2000020000000000
χ1922222-2-22-2-22222-2-22-2-22220000000000-2-2222-2-2220000-20000000000
χ2022222-2-22-2-22222-2-22-2-22-2-20000000000-2-222-222-2-2000020000000000
χ21222-2-22-2200222022-2-2-2-200000000000000002-22-202i−2i2i−2i00000000000
χ22222-2-22-2200222022-2-2-2-200000000000000002-22-20−2i2i−2i2i00000000000
χ23222-2-22-2200222022-2-2-2-20000000000000000-22-2202-2-2200000000000
χ24222-2-22-2200222022-2-2-2-20000000000000000-22-220-222-200000000000
χ25222-2-2-222002220-2-2-222-2000000000000000022-2-20000002i−2i2i−2i000000
χ26222-2-2-222002220-2-2-222-2000000000000000022-2-2000000−2i2i−2i2i000000
χ27222-2-2-222002220-2-2-222-20000000000000000-2-2220000002-2-22000000
χ28222-2-2-222002220-2-2-222-20000000000000000-2-222000000-222-2000000
χ294444444-144-1-1-14-1-1-1-1-1-10044-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ304444444-144-1-1-14-1-1-1-1-1-100-4-411111111-1-1-1-100000000000000000000
χ314444444-1-4-4-1-1-1-4-1-1-1-1-1-1004-4-1-1-1-11111111100000000000000000000
χ324444444-1-4-4-1-1-1-4-1-1-1-1-1-100-441111-1-1-1-1111100000000000000000000
χ3344444-4-4-144-1-1-1-411-111-1000055−5−555−5−5-1-11100000000000000000000
χ3444444-4-4-144-1-1-1-411-111-10000−5−555−5−555-1-11100000000000000000000
χ3544444-4-4-1-4-4-1-1-1411-111-1000055−5−5−5−55511-1-100000000000000000000
χ3644444-4-4-1-4-4-1-1-1411-111-10000−5−55555−5−511-1-100000000000000000000
χ3744-44-40044i−4i4-4-4000400-40000000000004i−4i0000000000000000000000
χ3844-44-4004−4i4i4-4-4000400-4000000000000−4i4i0000000000000000000000
χ3944-44-400-14i−4i-11105−5-15−510000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−iii5−i500000000000000000000
χ4044-44-400-14i−4i-11105−5-15−510000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−iii5−i500000000000000000000
χ4144-44-400-14i−4i-1110−55-1−5510000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ii−i5i500000000000000000000
χ4244-44-400-14i−4i-1110−55-1−5510000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ii−i5i500000000000000000000
χ4344-44-400-1−4i4i-11105−5-15−510000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38i−i−i5i500000000000000000000
χ4444-44-400-1−4i4i-11105−5-15−510000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38i−i−i5i500000000000000000000
χ4544-44-400-1−4i4i-1110−55-1−5510000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38i−ii5−i500000000000000000000
χ4644-44-400-1−4i4i-1110−55-1−5510000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38i−ii5−i500000000000000000000
χ4744-4-44004004-4-4000-400444000000000000000000-4000000000000000
χ4844-4-44004004-4-4000-4004-4-40000000000000000004000000000000000
χ49888-8-88-8-200-2-2-20-2-22222000000000000000000000000000000000000
χ50888-8-8-88-200-2-2-20222-2-22000000000000000000000000000000000000
χ5188-8-8800-200-222025−252−2525-2000000000000000000000000000000000000
χ5288-8-8800-200-2220−2525225−25-2000000000000000000000000000000000000
χ538-800000800-800000000042−420000000000000000000000000000000000
χ548-800000800-8000000000−42420000000000000000000000000000000000
χ5516-1600000-400445−450000000000000000000000000000000000000000000
χ5616-1600000-4004−45450000000000000000000000000000000000000000000

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