Finite Group Databasebeta

← Group #13020216

Character table — Group #13020216

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444444488888881010101016161616161616161616161616162020202020202020404040404040404040404080808080
order12224422245101010410102020202044442810101010101020204040404044448888488888888882888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111-1-111-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-11111-1-111
χ5111111111111111111111-1-1-1-111111111111111-1-1-1-1ii−i−i-1i−iii−i−iii−i−i-1-1i−i
χ6111111111111111111111-1-1-1-111111111111111-1-1-1-1−i−iii-1−ii−i−iii−i−iii-1-1−ii
χ7111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1ii−i−i-1i−iii−i−i−i−iii11−ii
χ8111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1−i−iii-1−ii−i−iiiii−i−i11i−i
χ91111111-1-111111-111111111111-1-1-11111-1-1-1-1-1-11-1-111111-111-1-1-1-1-1-1-1-11-111
χ101111111-1-111111-111111111111-1-1-11111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1111111111-1-1-1
χ111111111-1-111111-11111111111-11-1-1-1-1-1-1-1-111111-1-111111-111-1-1-1-11111-11-1-1
χ121111111-1-111111-11111111111-11-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-11111-1-1-1-1-1111
χ131111111-1-111111-1111111-1-1-1-11-1-1-11111-1-1-1-1-1-1-111-1ii−i−i1i−i−i−iii−i−iii-11i−i
χ141111111-1-111111-1111111-1-1-1-11-1-1-11111-1-1-1-1-1-1-111-1−i−iii1−iiii−i−iii−i−i-11−ii
χ151111111-1-111111-1111111-1-1-1-1-11-1-1-1-1-1-1-1-11111-111-1ii−i−i1i−i−i−iiiii−i−i1-1−ii
χ161111111-1-111111-1111111-1-1-1-1-11-1-1-1-1-1-1-1-11111-111-1−i−iii1−iiii−i−i−i−iii1-1i−i
χ17222222-222-22222-2-2-22-2-222-22-200220000-2-20000-2-2-220000200000000000000
χ18222222-222-22222-2-2-22-2-22-22-2200220000-2-20000222-20000-200000000000000
χ19222222-2-2-2-222222-2-22-2-222-22-200-2-20000220000-22220000-200000000000000
χ20222222-2-2-2-222222-2-22-2-22-22-2200-2-200002200002-2-2-20000200000000000000
χ212222-2-2200-22222022-2-2-2-22-22-200000000000000200-200000002i−2i2i−2i00000000
χ222222-2-2200-22222022-2-2-2-22-22-200000000000000200-20000000−2i2i−2i2i00000000
χ232222-2-2200-22222022-2-2-2-2-22-2200000000000000-200200000002-2-2200000000
χ242222-2-2200-22222022-2-2-2-2-22-2200000000000000-20020000000-222-200000000
χ252222-2-2-200222220-2-2-222-2222200000000000000-200-222220-2-2000000000000
χ262222-2-2-200222220-2-2-222-2222200000000000000-200-2-2-2-2-2022000000000000
χ272222-2-2-200222220-2-2-222-2-2-2-2-20000000000000020022i2i−2i−2i0−2i2i000000000000
χ282222-2-2-200222220-2-2-222-2-2-2-2-2000000000000002002−2i−2i2i2i02i−2i000000000000
χ294444444444-1-1-1-14-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ304444444444-1-1-1-14-1-1-1-1-1-10000-4-4-1-11111-1-1111100000000000000000000000
χ314444444-4-44-1-1-1-1-4-1-1-1-1-1-100004-411-1-1-1-111111100000000000000000000000
χ324444444-4-44-1-1-1-1-4-1-1-1-1-1-10000-4411111111-1-1-1-100000000000000000000000
χ33444444-444-4-1-1-1-1-411-111-1000000-1-155−5−51155−5−500000000000000000000000
χ34444444-444-4-1-1-1-1-411-111-1000000-1-1−5−55511−5−55500000000000000000000000
χ35444444-4-4-4-4-1-1-1-1411-111-10000001155−5−5-1-1−5−55500000000000000000000000
χ36444444-4-4-4-4-1-1-1-1411-111-100000011−5−555-1-155−5−500000000000000000000000
χ3744-4-44-400004-4-44000400-400000000000000000004i−4i00000000000000000000
χ3844-4-44-400004-4-44000400-40000000000000000000−4i4i00000000000000000000
χ3944-4-4-4404-404-4-44000-40040000004-4000000000000000000000000000000000
χ4044-4-4-4404-40-111-105−515−5-1000000-11−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ365−5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000000
χ4144-4-4-4404-40-111-105−515−5-1000000-11ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ365−5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000
χ4244-4-4-4404-40-111-10−551−55-1000000-11−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−55−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000000
χ4344-4-4-4404-40-111-10−551−55-1000000-11ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−55ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000000
χ4444-4-4-440-4404-4-44000-4004000000-44000000000000000000000000000000000
χ4544-4-4-440-440-111-105−515−5-10000001-1−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−55ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000
χ4644-4-4-440-440-111-105−515−5-10000001-1ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−55−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000000
χ4744-4-4-440-440-111-10−551−55-10000001-1−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ365−5ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000000
χ4844-4-4-440-440-111-10−551−55-10000001-1ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ365−5−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000000
χ494-44-400000044-4-40000000040-4000000000000000000000000000002i−2i2i−2i0000
χ504-44-400000044-4-40000000040-400000000000000000000000000000−2i2i−2i2i0000
χ514-44-400000044-4-400000000-404000000000000000000000000000002-2-220000
χ524-44-400000044-4-400000000-40400000000000000000000000000000-222-20000
χ534-4-440000004-44-4000000040-400000000000000000002i2−2i22i2−2i2000000000000000
χ544-4-440000004-44-4000000040-40000000000000000000−2i22i2−2i22i2000000000000000
χ554-4-440000004-44-40000000-404000000000000000000022−22−2222000000000000000
χ564-4-440000004-44-40000000-4040000000000000000000−222222−22000000000000000
χ578888-8-8800-8-2-2-2-20-2-2222200000000000000000000000000000000000000000
χ588888-8-8-8008-2-2-2-20222-2-2200000000000000000000000000000000000000000
χ5988-8-88-80000-222-2025−25-2−2525200000000000000000000000000000000000000000
χ6088-8-88-80000-222-20−2525-225−25200000000000000000000000000000000000000000
χ6116-1616-16000000-4-444000000000000000000000000000000000000000000000000
χ6216-16-1616000000-44-44000000000000000000000000000000000000000000000000

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