Finite Group Databasebeta

← Group #13021310

Character table — Group #13021310

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222244444444444448888888888881010101010101616161616161616161620202020204040404040404040808080808080
order12222244458888101010101010102020202040404040404040402244444420202020202020202888844448888248888
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
χ5111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1ii−i−iii−i−i-1-1ii−i−i
χ6111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1−i−iii−i−iii-1-1−i−iii
χ7111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−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−iii−i−iii11ii−i−i
χ91111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111111-11111-1-1-1-11-1-1-1-11111-1-1-1-11-11-11-1
χ101111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11111111-11111-1-1-1-11-1-1-1-1-1-1-1-111111-1-11-11
χ111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-11-1-1-1-111111-1-1-1-11111-1-1-1-1-11-11-11
χ121111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-11-1-1-1-111111-1-1-1-1-1-1-1-11111-111-11-1
χ131111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-11111ii−i−i−i−iii-11i−i−ii
χ141111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-11111−i−iiiii−i−i-11−iii−i
χ151111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-11111ii−i−i−i−iii1-1−iii−i
χ161111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-11111−i−iiiii−i−i1-1i−i−ii
χ17222222-2-2-2200002222222-2-2-2-20000000022-2-2-2-200000000002000000002i−2i2i−2i000000
χ18222222-2-2-2200002222222-2-2-2-20000000022-2-2-2-20000000000200000000−2i2i−2i2i000000
χ19222222-2-2-2200002222222-2-2-2-200000000-2-222220000000000-2000000002-2-22000000
χ20222222-2-2-2200002222222-2-2-2-200000000-2-222220000000000-200000000-222-2000000
χ212222-2-222-2222-2-22-2-2-2-2222-2-222222-2-2-2-22222-2-20000000000-222-2-200000000000000
χ222222-2-222-2222-2-22-2-2-2-2222-2-222222-2-2-2-2-2-2-2-22200000000002-2-22200000000000000
χ232222-2-222-22-2-2222-2-2-2-2222-2-22-2-2-2-222222222-2-20000000000-2-2-22200000000000000
χ242222-2-222-22-2-2222-2-2-2-2222-2-22-2-2-2-22222-2-2-2-2220000000000222-2-200000000000000
χ252222-2-2-2-22200002-2-2-2-222-222-20000000022-2-2220000000000-200002-22-20000000000
χ262222-2-2-2-22200002-2-2-2-222-222-20000000022-2-2220000000000-20000-22-220000000000
χ272222-2-2-2-22200002-2-2-2-222-222-200000000-2-222-2-20000000000200002i−2i−2i2i0000000000
χ282222-2-2-2-22200002-2-2-2-222-222-200000000-2-222-2-2000000000020000−2i2i2i−2i0000000000
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
χ31444444444-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1111111110000004-4-1-1-1-111110000000000000000000
χ32444444444-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-111111111000000-441111-1-1-1-10000000000000000000
χ334444-4-444-4-144-4-4-11111-1-1-111-1-1-1-1-111110000000055−5−555−5−50000000000000000000
χ344444-4-444-4-144-4-4-11111-1-1-111-1-1-1-1-1111100000000−5−555−5−5550000000000000000000
χ354444-4-444-4-1-4-444-11111-1-1-111-11111-1-1-1-10000000055−5−5−5−5550000000000000000000
χ364444-4-444-4-1-4-444-11111-1-1-111-11111-1-1-1-100000000−5−55555−5−50000000000000000000
χ3744-4-4000004002i2−2i2-400004-4000000002i22i2−2i2−2i24-4000000000000000002i2−2i200000000000000
χ3844-4-4000004002i2−2i2-400004-4000000002i22i2−2i2−2i2-4400000000000000000−2i22i200000000000000
χ3944-4-400000400−2i22i2-400004-400000000−2i2−2i22i22i24-400000000000000000−2i22i200000000000000
χ4044-4-400000400−2i22i2-400004-400000000−2i2−2i22i22i2-44000000000000000002i2−2i200000000000000
χ414-44-4004-4044i−4i00-40000-44400-44i4i−4i−4i000000000000000000000000000000000000000
χ424-44-4004-404−4i4i00-40000-44400-4−4i−4i4i4i000000000000000000000000000000000000000
χ434-44-4004-40-14i−4i00155−5−51-1-15−51−i−iiii5−i5i5−i500000000−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−ζ360000000000000000000
χ444-44-4004-40-14i−4i00155−5−51-1-15−51−i−iiii5−i5i5−i500000000ζ6−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+ζ360000000000000000000
χ454-44-4004-40-14i−4i001−5−5551-1-1−551−i−iii−i5i5−i5i500000000ζ6−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−ζ360000000000000000000
χ464-44-4004-40-14i−4i001−5−5551-1-1−551−i−iii−i5i5−i5i500000000−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+ζ360000000000000000000
χ474-44-4004-40-1−4i4i00155−5−51-1-15−51ii−i−i−i5i5−i5i500000000−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+ζ360000000000000000000
χ484-44-4004-40-1−4i4i00155−5−51-1-15−51ii−i−i−i5i5−i5i500000000ζ6−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−ζ360000000000000000000
χ494-44-4004-40-1−4i4i001−5−5551-1-1−551ii−i−ii5−i5i5−i500000000ζ6−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+ζ360000000000000000000
χ504-44-4004-40-1−4i4i001−5−5551-1-1−551ii−i−ii5−i5i5−i500000000−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−ζ360000000000000000000
χ514-44-400-44040000-40000-44-400400000000000000000000000004-40000000000000000
χ524-44-400-44040000-40000-44-40040000000000000000000000000-440000000000000000
χ534-4-444-40004000044-44-4-4-4000000000000004i−4i4i−4i00000000000000000000000000000
χ544-4-444-40004000044-44-4-4-400000000000000−4i4i−4i4i00000000000000000000000000000
χ554-4-44-44000400004-44-44-4-4000000000000004i−4i−4i4i00000000000000000000000000000
χ564-4-44-44000400004-44-44-4-400000000000000−4i4i4i−4i00000000000000000000000000000
χ57888888-8-8-8-20000-2-2-2-2-2-2-222220000000000000000000000000000000000000000000
χ588888-8-8-8-88-20000-22222-2-22-2-220000000000000000000000000000000000000000000
χ5988-8-800000-2004i2−4i2225−25−2525-220000i10−i10i10−i10−i2−i2i2i200000000000000000000000000000000000
χ6088-8-800000-2004i2−4i22−252525−25-220000−i10i10−i10i10−i2−i2i2i200000000000000000000000000000000000
χ6188-8-800000-200−4i24i2225−25−2525-220000−i10i10−i10i10i2i2−i2−i200000000000000000000000000000000000
χ6288-8-800000-200−4i24i22−252525−25-220000i10−i10i10−i10i2i2−i2−i200000000000000000000000000000000000
χ638-88-800-880-2000022525−25−252-22−2525-20000000000000000000000000000000000000000000
χ648-88-800-880-200002−25−2525252-2225−25-20000000000000000000000000000000000000000000
χ658-8-888-8000-20000-2-22-2222000010−10−101010−10−101000000000000000000000000000000000000
χ668-8-888-8000-20000-2-22-22220000−101010−10−101010−1000000000000000000000000000000000000
χ678-8-88-88000-20000-22-22-222000010−10−1010−101010−1000000000000000000000000000000000000
χ688-8-88-88000-20000-22-22-2220000−101010−1010−10−101000000000000000000000000000000000000

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