Finite Group Databasebeta

← Group #13013790

Character table — Group #13013790

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222244444444444448888888888881010101010101616161616161616161620202020204040404040404040808080808080
order1222444425888810101020202020101020204040404040404040228888884040404040404040244881616161616161616444488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1iiii−i−i−i−iii−i−i-1-1
χ6111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1−i−i−i−iiiii−i−iii-1-1
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−i−i−iii11
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−iiiiiii−i−i11
χ9111111-1-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1i−iiiii−i−i−i−i-11-111ii−i−iii−i−i1-11-1i−i
χ10111111-1-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1i−iiiii−i−i−i−i-11-111−i−iii−i−iii-11-11i−i
χ11111111-1-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1−ii−i−i−i−iiiii-11-111ii−i−iii−i−i-11-11−ii
χ12111111-1-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1−ii−i−i−i−iiiii-11-111−i−iii−i−iii1-11-1−ii
χ13111111-1-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-11111i−iiiii−i−i−i−i1-11-1-111-1-1-1-111−iii−i−ii
χ14111111-1-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-11111i−iiiii−i−i−i−i1-11-1-1-1-11111-1-1i−i−ii−ii
χ15111111-1-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-11111−ii−i−i−i−iiiii1-11-1-111-1-1-1-111i−i−iii−i
χ16111111-1-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-11111−ii−i−i−i−iiiii1-11-1-1-1-11111-1-1−iii−ii−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
χ19222222-2-2-22-2-222222-2-2-2-2-2-222-2-2-2-222222222220000000000-22-2-2-200000000000000
χ20222222-2-2-22-2-222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-200000000002-222200000000000000
χ212222-2-222-2200002222222-2-2-2-2000000002200000000000000-2-22002−22−22−22−2000000
χ222222-2-222-2200002222222-2-2-2-2000000002200000000000000-2-2200−22−22−22−22000000
χ232222-2-222-2200002222222-2-2-2-200000000-2-20000000000000022-200i2−i2i2−i2−i2i2−i2i2000000
χ242222-2-222-2200002222222-2-2-2-200000000-2-20000000000000022-200−i2i2−i2i2i2−i2i2−i2000000
χ252222-2-2-2-2220000222-2-2-2-222-2-20000000022000000000000002-2-200i2−i2−i2i2i2−i2−i2i2000000
χ262222-2-2-2-2220000222-2-2-2-222-2-20000000022000000000000002-2-200−i2i2i2−i2−i2i2i2−i2000000
χ272222-2-2-2-2220000222-2-2-2-222-2-200000000-2-200000000000000-222002−2−22−222−2000000
χ282222-2-2-2-2220000222-2-2-2-222-2-200000000-2-200000000000000-22200−222−22−2−22000000
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
χ33444444-4-4-4-144-4-4-1-1-1111111-1-1-1-1-1-111110000004i−4i−i−i−i−iiiii0000000000000000000
χ34444444-4-4-4-144-4-4-1-1-1111111-1-1-1-1-1-11111000000−4i4iiiii−i−i−i−i0000000000000000000
χ35444444-4-4-4-1-4-444-1-1-1111111-1-11111-1-1-1-100000000i5i5−i5−i5−i5−i5i5i50000000000000000000
χ36444444-4-4-4-1-4-444-1-1-1111111-1-11111-1-1-1-100000000−i5−i5i5i5i5i5−i5−i50000000000000000000
χ3744-4-40000040022−224-4-40000000000002222−22−224-42222−22−2200000000000000000000000000000
χ3844-4-40000040022−224-4-40000000000002222−22−22-44−22−22222200000000000000000000000000000
χ3944-4-400000400−22224-4-4000000000000−22−2222224-4−22−22222200000000000000000000000000000
χ4044-4-400000400−22224-4-4000000000000−22−222222-442222−22−2200000000000000000000000000000
χ414-44-4004i−4i040000-44-44i4i−4i−4i0000000000000022−2222−2200000000000002i2−2i200000000000000
χ424-44-4004i−4i040000-44-44i4i−4i−4i00000000000000−2222−22220000000000000−2i22i200000000000000
χ434-44-400−4i4i040000-44-4−4i−4i4i4i0000000000000022−2222−220000000000000−2i22i200000000000000
χ444-44-400−4i4i040000-44-4−4i−4i4i4i00000000000000−2222−222200000000000002i2−2i200000000000000
χ454-4-444-400044i−4i00-4-440000004-44i4i−4i−4i000000000000000000000000000000000000000
χ464-4-444-40004−4i4i00-4-440000004-4−4i−4i4i4i000000000000000000000000000000000000000
χ474-4-444-4000-14i−4i0011-15−55−55−5-11−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
χ484-4-444-4000-14i−4i0011-15−55−55−5-11−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
χ494-4-444-4000-14i−4i0011-1−55−55−55-11−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
χ504-4-444-4000-14i−4i0011-1−55−55−55-11−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
χ514-4-444-4000-1−4i4i0011-15−55−55−5-11ii−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
χ524-4-444-4000-1−4i4i0011-15−55−55−5-11ii−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
χ534-4-444-4000-1−4i4i0011-1−55−55−55-11ii−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
χ544-4-444-4000-1−4i4i0011-1−55−55−55-11ii−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
χ554-4-44-4400040000-4-44000000-4400000000004-4-4400000000000000000000000000000
χ564-4-44-4400040000-4-44000000-440000000000-444-400000000000000000000000000000
χ578888-8-888-8-20000-2-2-2-2-2-2-222220000000000000000000000000000000000000000000
χ588888-8-8-8-88-20000-2-2-22222-2-2220000000000000000000000000000000000000000000
χ5988-8-800000-20042−42-2222i5−2i5−2i52i50000i10−i10i10−i10−2−22200000000000000000000000000000000000
χ6088-8-800000-20042−42-222−2i52i52i5−2i50000−i10i10−i10i10−2−22200000000000000000000000000000000000
χ6188-8-800000-200−4242-2222i5−2i5−2i52i50000−i10i10−i10i1022−2−200000000000000000000000000000000000
χ6288-8-800000-200−4242-222−2i52i52i5−2i50000i10−i10i10−i1022−2−200000000000000000000000000000000000
χ638-88-8008i−8i0-200002-22−2i−2i2i2i000010−10−1010−i10i10i10−i1000000000000000000000000000000000000
χ648-88-8008i−8i0-200002-22−2i−2i2i2i0000−101010−10i10−i10−i10i1000000000000000000000000000000000000
χ658-88-800−8i8i0-200002-222i2i−2i−2i000010−10−1010i10−i10−i10i1000000000000000000000000000000000000
χ668-88-800−8i8i0-200002-222i2i−2i−2i0000−101010−10−i10i10i10−i1000000000000000000000000000000000000
χ678-8-88-88000-2000022-225−2525−25−25252-20000000000000000000000000000000000000000000
χ688-8-88-88000-2000022-2−2525−252525−252-20000000000000000000000000000000000000000000

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