Finite Group Databasebeta

← Group #13027040

Character table — Group #13027040

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222444444448888888161616161616161616161616161620202020202040404040404040404040408080808080
order12244244451010102101020202020481010202020202020404040402244444444444448844488
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1i−ii−i
χ41111111111111111111111111111111111-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1−ii−ii
χ511111111111111111111-1-11111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i111−ii−ii
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii111i−ii−i
χ91111111-1-11111-11111111-1-1-1-1-11111-1-1-1-1111-1-11-111-1-111-1-1-1-1111-1-1
χ101111111-1-11111-11111111-1-1-1-1-11111-1-1-1-1111-1-11-1-1-111-1-111-1-11-1-111
χ111111111-1-11111-11111111-1-1-1-1-11111-1-1-1-1-1-1-111-11ii−i−i−i−iii11-1i−i−ii
χ121111111-1-11111-11111111-1-1-1-1-11111-1-1-1-1-1-1-111-11−i−iiiii−i−i11-1−iii−i
χ131111111-1-11111-1111111-11-1-1-1-1-1-1-1-11111111-1-11-111-1-111-1-111-1-1-111
χ141111111-1-11111-1111111-11-1-1-1-1-1-1-1-11111111-1-11-1-1-111-1-11111-111-1-1
χ151111111-1-11111-1111111-11-1-1-1-1-1-1-1-11111-1-1-111-11ii−i−i−i−iii-1-11−iii−i
χ161111111-1-11111-1111111-11-1-1-1-1-1-1-1-11111-1-1-111-11−i−iiiii−i−i-1-11i−i−ii
χ1722222-2-2222222-2-2-22-2-2200-2-222000000002-2-2-2-222000000000000000
χ1822222-2-2222222-2-2-22-2-2200-2-22200000000-22222-2-2000000000000000
χ1922222-2-2-2-222222-2-22-2-220022-2-2000000002-2-2222-2000000000000000
χ2022222-2-2-2-222222-2-22-2-220022-2-200000000-222-2-2-22000000000000000
χ21222-2-22-2002222022-2-2-2-2000000000000002-2200-20002i−2i002i−2i0000000
χ22222-2-22-2002222022-2-2-2-2000000000000002-2200-2000−2i2i00−2i2i0000000
χ23222-2-22-2002222022-2-2-2-200000000000000-22-20020002-200-220000000
χ24222-2-22-2002222022-2-2-2-200000000000000-22-2002000-22002-20000000
χ25222-2-2-220022220-2-2-222-20000000000000022-200-202-2002-2000000000
χ26222-2-2-220022220-2-2-222-20000000000000022-200-20-2200-22000000000
χ27222-2-2-220022220-2-2-222-200000000000000-2-2200202i−2i00−2i2i000000000
χ28222-2-2-220022220-2-2-222-200000000000000-2-220020−2i2i002i−2i000000000
χ29444444444-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ30444444444-1-1-1-14-1-1-1-1-1-1-4-4-1-1-1-1111111110000000000000000000000
χ314444444-4-4-1-1-1-1-4-1-1-1-1-1-14-41111-1-1-1-111110000000000000000000000
χ324444444-4-4-1-1-1-1-4-1-1-1-1-1-1-4411111111-1-1-1-10000000000000000000000
χ3344444-4-444-1-1-1-1-411-111-10011-1-155−5−555−5−50000000000000000000000
χ3444444-4-444-1-1-1-1-411-111-10011-1-1−5−555−5−5550000000000000000000000
χ3544444-4-4-4-4-1-1-1-1411-111-100-1-11155−5−5−5−5550000000000000000000000
χ3644444-4-4-4-4-1-1-1-1411-111-100-1-111−5−55555−5−50000000000000000000000
χ3744-44-4004-44-4-44000-400400004-4000000000000000000000000000000
χ3844-44-4004-4-111-105−515−5-1005−5-11−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
χ3944-44-4004-4-111-105−515−5-1005−5-11ζ4−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
χ4044-44-4004-4-111-10−551−55-100−55-11−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
χ4144-44-4004-4-111-10−551−55-100−55-11ζ4+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
χ4244-44-400-444-4-44000-40040000-44000000000000000000000000000000
χ4344-44-400-44-111-105−515−5-100−551-1−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000000000000
χ4444-44-400-44-111-105−515−5-100−551-1ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ360000000000000000000000
χ4544-44-400-44-111-10−551−55-1005−51-1−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ360000000000000000000000
χ4644-44-400-44-111-10−551−55-1005−51-1ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000000000000
χ4744-4-4400004-4-44000400-4000000000000000004-400000000000000000
χ4844-4-4400004-4-44000400-400000000000000000-4400000000000000000
χ49888-8-88-800-2-2-2-20-2-22222000000000000000000000000000000000000
χ50888-8-8-8800-2-2-2-20222-2-22000000000000000000000000000000000000
χ5188-8-880000-222-2025−25-2−25252000000000000000000000000000000000000
χ5288-8-880000-222-20−2525-225−252000000000000000000000000000000000000
χ538-80000000800-800000000000000000000000000000000000022−2200000
χ548-80000000800-8000000000000000000000000000000000000−222200000
χ5516-160000000-445−4540000000000000000000000000000000000000000000
χ5616-160000000-4−454540000000000000000000000000000000000000000000

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