Finite Group Databasebeta

← Group #13020210

Character table — Group #13020210

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444444488888881010101016161616161616161616161616162020202020202020404040404040404040404080808080
order12224424445101010410102020202044444820202020202020204040404044448888288888888884888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111-1-11111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-11111-1-111
χ5111111111111111111111-1-1-1-111111111111111-1-1-1-1ii−i−i-1iii−i−i−iii−i−i-1-1i−i
χ6111111111111111111111-1-1-1-111111111111111-1-1-1-1−i−iii-1−i−i−iiii−i−iii-1-1−ii
χ7111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1iii−i−i−i−i−iii11−ii
χ8111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1−i−i−iiiiii−i−i11i−i
χ911111111-1-11111-111111111111-1-1-1-1-11111-1-1-1-1-1-1111111-11-1-11-1-1-1-1-1-11-111
χ1011111111-1-11111-111111111111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-11111111-1-1-1
χ1111111111-1-11111-11111111111-11-1-1-1-1-1-1-1-11111-1-1111111-11-1-11-1-11111-11-1-1
χ1211111111-1-11111-11111111111-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-111-1-1-1-1-1111
χ1311111111-1-11111-1111111-1-1-1-11-1-1-1-1-11111-1-1-1-111-1-1ii−i−i1i−i−i−iii−i−iii-11i−i
χ1411111111-1-11111-1111111-1-1-1-11-1-1-1-1-11111-1-1-1-111-1-1−i−iii1−iiii−i−iii−i−i-11−ii
χ1511111111-1-11111-1111111-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1ii−i−i1i−i−i−iiiii−i−i1-1−ii
χ1611111111-1-11111-1111111-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1−i−iii1−iiii−i−i−i−iii1-1i−i
χ17222222-2-2222222-2-2-22-2-222-22-200-2-22200000000-2-2-220000200000000000000
χ18222222-2-2222222-2-2-22-2-22-22-2200-2-22200000000222-20000-200000000000000
χ19222222-2-2-2-222222-2-22-2-222-22-20022-2-20000000022-220000-200000000000000
χ20222222-2-2-2-222222-2-22-2-22-22-220022-2-200000000-2-22-20000200000000000000
χ212222-2-22-2002222022-2-2-2-22-22-200000000000000002-20000002i−2i02i−2i00000000
χ222222-2-22-2002222022-2-2-2-22-22-200000000000000002-2000000−2i2i0−2i2i00000000
χ232222-2-22-2002222022-2-2-2-2-22-220000000000000000-220000002-20-2200000000
χ242222-2-22-2002222022-2-2-2-2-22-220000000000000000-22000000-2202-200000000
χ252222-2-2-220022220-2-2-222-222220000000000000000-2-222220-200-20000000000
χ262222-2-2-220022220-2-2-222-222220000000000000000-2-2-2-2-2-2020020000000000
χ272222-2-2-220022220-2-2-222-2-2-2-2-20000000000000000222i2i−2i−2i0−2i002i0000000000
χ282222-2-2-220022220-2-2-222-2-2-2-2-2000000000000000022−2i−2i2i2i02i00−2i0000000000
χ294444444444-1-1-1-14-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ304444444444-1-1-1-14-1-1-1-1-1-10000-4-4-1-1-1-11111111100000000000000000000000
χ3144444444-4-4-1-1-1-1-4-1-1-1-1-1-100004-41111-1-1-1-1111100000000000000000000000
χ3244444444-4-4-1-1-1-1-4-1-1-1-1-1-10000-4411111111-1-1-1-100000000000000000000000
χ33444444-4-444-1-1-1-1-411-111-100000011-1-155−5−555−5−500000000000000000000000
χ34444444-4-444-1-1-1-1-411-111-100000011-1-1−5−555−5−55500000000000000000000000
χ35444444-4-4-4-4-1-1-1-1411-111-1000000-1-11155−5−5−5−55500000000000000000000000
χ36444444-4-4-4-4-1-1-1-1411-111-1000000-1-111−5−55555−5−500000000000000000000000
χ3744-4-400000044-4-40000000040-4000000000000000000000000000002-22-20000
χ3844-4-400000044-4-40000000040-400000000000000000000000000000-22-220000
χ3944-4-400000044-4-400000000-404000000000000000000000000000002i−2i−2i2i0000
χ4044-4-400000044-4-400000000-40400000000000000000000000000000−2i2i2i−2i0000
χ414-44-44-400004-44-4000400-40000000000000000004-4000000000000000000000
χ424-44-44-400004-44-4000400-4000000000000000000-44000000000000000000000
χ434-44-4-44004i−4i4-44-4000-4004000000004i−4i0000000000000000000000000000000
χ444-44-4-44004i−4i-11-1105−515−5-1000000i5−i5−ii−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000000
χ454-44-4-44004i−4i-11-1105−515−5-1000000i5−i5−iiζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000
χ464-44-4-44004i−4i-11-110−551−55-1000000−i5i5−iiζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000000
χ474-44-4-44004i−4i-11-110−551−55-1000000−i5i5−ii−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000000
χ484-44-4-4400−4i4i4-44-4000-400400000000−4i4i0000000000000000000000000000000
χ494-44-4-4400−4i4i-11-1105−515−5-1000000−i5i5i−i−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000
χ504-44-4-4400−4i4i-11-1105−515−5-1000000−i5i5i−iζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000000
χ514-44-4-4400−4i4i-11-110−551−55-1000000i5−i5i−iζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000000
χ524-44-4-4400−4i4i-11-110−551−55-1000000i5−i5i−i−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000000
χ534-4-440000004-4-44000000040-400000000000000000002i2−2i22i2−2i2000000000000000
χ544-4-440000004-4-44000000040-40000000000000000000−2i22i2−2i22i2000000000000000
χ554-4-440000004-4-440000000-404000000000000000000022−22−2222000000000000000
χ564-4-440000004-4-440000000-4040000000000000000000−222222−22000000000000000
χ578888-8-88-800-2-2-2-20-2-2222200000000000000000000000000000000000000000
χ588888-8-8-8800-2-2-2-20222-2-2200000000000000000000000000000000000000000
χ598-88-88-80000-22-22025−25-2−2525200000000000000000000000000000000000000000
χ608-88-88-80000-22-220−2525-225−25200000000000000000000000000000000000000000
χ611616-16-16000000-4-444000000000000000000000000000000000000000000000000
χ6216-16-1616000000-444-4000000000000000000000000000000000000000000000000

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