Finite Group Databasebeta

← Group #13013784

Character table — Group #13013784

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222244444444444448888888888881010101010101616161616161616161620202020204040404040404040808080808080
order1222224445888810101010101010202020204040404040404040228888442020202020202020244881616161616161616444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ6111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ7111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ8111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ91111-1-111-1111-1-111-1-11-1-11-1-111111-1-1-1-111-1-1-1-1i−iiiii−i−i−i−i-11-111ii−i−iii−i−ii−i1-11-1
χ101111-1-111-1111-1-111-1-11-1-11-1-111111-1-1-1-111-1-1-1-1i−iiiii−i−i−i−i-11-111−i−iii−i−iiii−i-11-11
χ111111-1-111-1111-1-111-1-11-1-11-1-111111-1-1-1-111-1-1-1-1−ii−i−i−i−iiiii-11-111ii−i−iii−i−i−ii-11-11
χ121111-1-111-1111-1-111-1-11-1-11-1-111111-1-1-1-111-1-1-1-1−ii−i−i−i−iiiii-11-111−i−iii−i−iii−ii1-11-1
χ131111-1-111-1111-1-111-1-11-1-11-1-111111-1-1-1-1-1-11111i−iiiii−i−i−i−i1-11-1-111-1-1-1-111−ii−iii−i
χ141111-1-111-1111-1-111-1-11-1-11-1-111111-1-1-1-1-1-11111i−iiiii−i−i−i−i1-11-1-1-1-11111-1-1−iii−i−ii
χ151111-1-111-1111-1-111-1-11-1-11-1-111111-1-1-1-1-1-11111−ii−i−i−i−iiiii1-11-1-111-1-1-1-111i−ii−i−ii
χ161111-1-111-1111-1-111-1-11-1-11-1-111111-1-1-1-1-1-11111−ii−i−i−i−iiiii1-11-1-1-1-11111-1-1i−i−iii−i
χ172222222222-2-2-2-222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000222-2-200000000000000
χ182222222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-222220000000000-2-2-22200000000000000
χ19222222-2-2-2200002222222-2-2-2-20000000022000000000000002-2-2002−22−22−22−2000000
χ20222222-2-2-2200002222222-2-2-2-20000000022000000000000002-2-200−22−22−22−22000000
χ21222222-2-2-2200002222222-2-2-2-200000000-2-200000000000000-22200i2−i2i2−i2−i2i2−i2i2000000
χ22222222-2-2-2200002222222-2-2-2-200000000-2-200000000000000-22200−i2i2−i2i2i2−i2i2−i2000000
χ232222-2-222-22-2-22222-2-22-2-22-2-22-2-2-2-222222222220000000000-22-2-2-200000000000000
χ242222-2-222-22-2-22222-2-22-2-22-2-22-2-2-2-22222-2-2-2-2-2-200000000002-222200000000000000
χ252222-2-2-2-222000022-2-22-2-2-222-2000000002200000000000000-2-2200i2−i2−i2i2i2−i2−i2i2000000
χ262222-2-2-2-222000022-2-22-2-2-222-2000000002200000000000000-2-2200−i2i2i2−i2−i2i2i2−i2000000
χ272222-2-2-2-222000022-2-22-2-2-222-200000000-2-20000000000000022-2002−2−22−222−2000000
χ282222-2-2-2-222000022-2-22-2-2-222-200000000-2-20000000000000022-200−222−22−2−22000000
χ29444444444-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000044-1-1-1-1-1-1-1-10000000000000000000
χ30444444444-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-4-4111111110000000000000000000
χ31444444444-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1111111110000000055−5−555−5−50000000000000000000
χ32444444444-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-11111111100000000−5−555−5−5550000000000000000000
χ334444-4-444-4-144-4-4-1-111-111-111-1-1-1-1-111110000004i−4i−i−i−i−iiiii0000000000000000000
χ344444-4-444-4-144-4-4-1-111-111-111-1-1-1-1-11111000000−4i4iiiii−i−i−i−i0000000000000000000
χ354444-4-444-4-1-4-444-1-111-111-111-11111-1-1-1-100000000i5i5−i5−i5−i5−i5i5i50000000000000000000
χ364444-4-444-4-1-4-444-1-111-111-111-11111-1-1-1-100000000−i5−i5i5i5i5i5−i5−i50000000000000000000
χ3744-4-4000004002i2−2i24-400-400000000002i22i2−2i2−2i24-42i22i2−2i2−2i200000000000000000000000000000
χ3844-4-4000004002i2−2i24-400-400000000002i22i2−2i2−2i2-44−2i2−2i22i22i200000000000000000000000000000
χ3944-4-400000400−2i22i24-400-40000000000−2i2−2i22i22i24-4−2i2−2i22i22i200000000000000000000000000000
χ4044-4-400000400−2i22i24-400-40000000000−2i2−2i22i22i2-442i22i2−2i2−2i200000000000000000000000000000
χ414-44-44-400040000-44-4-4-444000000000000002i2−2i22i2−2i200000000000002i2−2i200000000000000
χ424-44-44-400040000-44-4-4-44400000000000000−2i22i2−2i22i20000000000000−2i22i200000000000000
χ434-44-4-4400040000-4444-4-4-4000000000000002i2−2i22i2−2i20000000000000−2i22i200000000000000
χ444-44-4-4400040000-4444-4-4-400000000000000−2i22i2−2i22i200000000000002i2−2i200000000000000
χ454-4-44004-4044i−4i00-4-400400400-44i4i−4i−4i000000000000000000000000000000000000000
χ464-4-44004-404−4i4i00-4-400400400-4−4i−4i4i4i000000000000000000000000000000000000000
χ474-4-44004-40-14i−4i00115−5-15−5-15−51−i−iiii5−i5i5−i500000000ζ6+ζ12−ζ14−ζ28−ζ6−ζ12+ζ14+ζ28−ζ4−ζ22+ζ36+ζ38ζ4+ζ22−ζ36−ζ38ζ6−ζ12−ζ14+ζ28−ζ6+ζ12+ζ14−ζ28−ζ4+ζ22+ζ36−ζ38ζ4−ζ22−ζ36+ζ380000000000000000000
χ484-4-44004-40-14i−4i00115−5-15−5-15−51−i−iiii5−i5i5−i500000000−ζ6−ζ12+ζ14+ζ28ζ6+ζ12−ζ14−ζ28ζ4+ζ22−ζ36−ζ38−ζ4−ζ22+ζ36+ζ38−ζ6+ζ12+ζ14−ζ28ζ6−ζ12−ζ14+ζ28ζ4−ζ22−ζ36+ζ38−ζ4+ζ22+ζ36−ζ380000000000000000000
χ494-4-44004-40-14i−4i0011−55-1−55-1−551−i−iii−i5i5−i5i500000000−ζ4−ζ22+ζ36+ζ38ζ4+ζ22−ζ36−ζ38−ζ6−ζ12+ζ14+ζ28ζ6+ζ12−ζ14−ζ28ζ4−ζ22−ζ36+ζ38−ζ4+ζ22+ζ36−ζ38ζ6−ζ12−ζ14+ζ28−ζ6+ζ12+ζ14−ζ280000000000000000000
χ504-4-44004-40-14i−4i0011−55-1−55-1−551−i−iii−i5i5−i5i500000000ζ4+ζ22−ζ36−ζ38−ζ4−ζ22+ζ36+ζ38ζ6+ζ12−ζ14−ζ28−ζ6−ζ12+ζ14+ζ28−ζ4+ζ22+ζ36−ζ38ζ4−ζ22−ζ36+ζ38−ζ6+ζ12+ζ14−ζ28ζ6−ζ12−ζ14+ζ280000000000000000000
χ514-4-44004-40-1−4i4i00115−5-15−5-15−51ii−i−i−i5i5−i5i500000000ζ6−ζ12−ζ14+ζ28−ζ6+ζ12+ζ14−ζ28ζ4−ζ22−ζ36+ζ38−ζ4+ζ22+ζ36−ζ38ζ6+ζ12−ζ14−ζ28−ζ6−ζ12+ζ14+ζ28ζ4+ζ22−ζ36−ζ38−ζ4−ζ22+ζ36+ζ380000000000000000000
χ524-4-44004-40-1−4i4i00115−5-15−5-15−51ii−i−i−i5i5−i5i500000000−ζ6+ζ12+ζ14−ζ28ζ6−ζ12−ζ14+ζ28−ζ4+ζ22+ζ36−ζ38ζ4−ζ22−ζ36+ζ38−ζ6−ζ12+ζ14+ζ28ζ6+ζ12−ζ14−ζ28−ζ4−ζ22+ζ36+ζ38ζ4+ζ22−ζ36−ζ380000000000000000000
χ534-4-44004-40-1−4i4i0011−55-1−55-1−551ii−i−ii5−i5i5−i500000000−ζ4+ζ22+ζ36−ζ38ζ4−ζ22−ζ36+ζ38ζ6−ζ12−ζ14+ζ28−ζ6+ζ12+ζ14−ζ28ζ4+ζ22−ζ36−ζ38−ζ4−ζ22+ζ36+ζ38−ζ6−ζ12+ζ14+ζ28ζ6+ζ12−ζ14−ζ280000000000000000000
χ544-4-44004-40-1−4i4i0011−55-1−55-1−551ii−i−ii5−i5i5−i500000000ζ4−ζ22−ζ36+ζ38−ζ4+ζ22+ζ36−ζ38−ζ6+ζ12+ζ14−ζ28ζ6−ζ12−ζ14+ζ28−ζ4−ζ22+ζ36+ζ38ζ4+ζ22−ζ36−ζ38ζ6+ζ12−ζ14−ζ28−ζ6−ζ12+ζ14+ζ280000000000000000000
χ554-4-4400-44040000-4-400400-400400000000004-4-4400000000000000000000000000000
χ564-4-4400-44040000-4-400400-40040000000000-444-400000000000000000000000000000
χ57888888-8-8-8-20000-2-2-2-2-2-2-222220000000000000000000000000000000000000000000
χ588888-8-8-8-88-20000-2-222-2222-2-220000000000000000000000000000000000000000000
χ5988-8-800000-2004i2−4i2-2225−252−25250000i10−i10i10−i10−i2−i2i2i200000000000000000000000000000000000
χ6088-8-800000-2004i2−4i2-22−2525225−250000−i10i10−i10i10−i2−i2i2i200000000000000000000000000000000000
χ6188-8-800000-200−4i24i2-2225−252−25250000−i10i10−i10i10i2i2−i2−i200000000000000000000000000000000000
χ6288-8-800000-200−4i24i2-22−2525225−250000i10−i10i10−i10i2i2−i2−i200000000000000000000000000000000000
χ638-88-88-8000-200002-2222-2-2000010−10−1010−101010−1000000000000000000000000000000000000
χ648-88-88-8000-200002-2222-2-20000−101010−1010−10−101000000000000000000000000000000000000
χ658-88-8-88000-200002-2-2-2222000010−10−101010−10−101000000000000000000000000000000000000
χ668-88-8-88000-200002-2-2-22220000−101010−10−101010−1000000000000000000000000000000000000
χ678-8-8800-880-200002225−25-225−252−2525-20000000000000000000000000000000000000000000
χ688-8-8800-880-2000022−2525-2−2525225−25-20000000000000000000000000000000000000000000

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