Finite Group Databasebeta

← Group #13021313

Character table — Group #13021313

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
χ212222-2-222-2222-2-2-2-2-2-22222-2-222222-2-2-2-22222-2-20000000000-222-2-200000000000000
χ222222-2-222-2222-2-2-2-2-2-22222-2-222222-2-2-2-2-2-2-2-22200000000002-2-22200000000000000
χ232222-2-222-22-2-222-2-2-2-22222-2-22-2-2-2-222222222-2-20000000000-2-2-22200000000000000
χ242222-2-222-22-2-222-2-2-2-22222-2-22-2-2-2-22222-2-2-2-2220000000000222-2-200000000000000
χ252222-2-2-2-2220000-2-2-2-2222-222-20000000022-2-2220000000000-200002-22-20000000000
χ262222-2-2-2-2220000-2-2-2-2222-222-20000000022-2-2220000000000-20000-22-220000000000
χ272222-2-2-2-2220000-2-2-2-2222-222-200000000-2-222-2-20000000000200002i−2i−2i2i0000000000
χ282222-2-2-2-2220000-2-2-2-2222-222-200000000-2-222-2-2000000000020000−2i2i2i−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
χ334444-4-444-4-144-4-41111-1-1-1-111-1-1-1-1-111110000000055−5−555−5−50000000000000000000
χ344444-4-444-4-144-4-41111-1-1-1-111-1-1-1-1-1111100000000−5−555−5−5550000000000000000000
χ354444-4-444-4-1-4-4441111-1-1-1-111-11111-1-1-1-10000000055−5−5−5−5550000000000000000000
χ364444-4-444-4-1-4-4441111-1-1-1-111-11111-1-1-1-100000000−5−55555−5−50000000000000000000
χ3744-4-4000004002i2−2i20000-44-4000000002i22i2−2i2−2i24-4000000000000000002i2−2i200000000000000
χ3844-4-4000004002i2−2i20000-44-4000000002i22i2−2i2−2i2-4400000000000000000−2i22i200000000000000
χ3944-4-400000400−2i22i20000-44-400000000−2i2−2i22i22i24-400000000000000000−2i22i200000000000000
χ4044-4-400000400−2i22i20000-44-400000000−2i2−2i22i22i2-44000000000000000002i2−2i200000000000000
χ414-44-44-40004000044-4-4-4-44000000000000004i−4i4i−4i00000000000000000000000000000
χ424-44-44-40004000044-4-4-4-4400000000000000−4i4i−4i4i00000000000000000000000000000
χ434-44-4-4400040000-4-444-4-44000000000000004i−4i−4i4i00000000000000000000000000000
χ444-44-4-4400040000-4-444-4-4400000000000000−4i4i4i−4i00000000000000000000000000000
χ454-4-44004-404000000004-4-4400-400000000000000000000000004i−4i0000000000000000
χ464-4-44004-404000000004-4-4400-40000000000000000000000000−4i4i0000000000000000
χ474-4-4400-44044-40000004-4-4-400444-4-4000000000000000000000000000000000000000
χ484-4-4400-4404-440000004-4-4-4004-4-444000000000000000000000000000000000000000
χ494-4-4400-440-14-4005−55−5-11115−5-1-1-1115−55−500000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000
χ504-4-4400-440-14-4005−55−5-11115−5-1-1-1115−55−500000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000
χ514-4-4400-440-14-400−55−55-1111−55-1-1-111−55−5500000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000
χ524-4-4400-440-14-400−55−55-1111−55-1-1-111−55−5500000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000
χ534-4-4400-440-1-44005−55−5-11115−5-111-1-1−55−5500000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000
χ544-4-4400-440-1-44005−55−5-11115−5-111-1-1−55−5500000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000
χ554-4-4400-440-1-4400−55−55-1111−55-111-1-15−55−500000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000
χ564-4-4400-440-1-4400−55−55-1111−55-111-1-15−55−500000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000
χ57888888-8-8-8-20000-2-2-2-2-2-2-222220000000000000000000000000000000000000000000
χ588888-8-8-8-88-200002222-2-2-22-2-220000000000000000000000000000000000000000000
χ5988-8-800000-2004i2−4i225−25−25252-220000i10−i10i10−i10−i2−i2i2i200000000000000000000000000000000000
χ6088-8-800000-2004i2−4i2−252525−252-220000−i10i10−i10i10−i2−i2i2i200000000000000000000000000000000000
χ6188-8-800000-200−4i24i225−25−25252-220000−i10i10−i10i10i2i2−i2−i200000000000000000000000000000000000
χ6288-8-800000-200−4i24i2−252525−252-220000i10−i10i10−i10i2i2−i2−i200000000000000000000000000000000000
χ638-88-88-8000-20000-2-22222-20000i10−i10−i10i10i10−i10−i10i1000000000000000000000000000000000000
χ648-88-88-8000-20000-2-22222-20000−i10i10i10−i10−i10i10i10−i1000000000000000000000000000000000000
χ658-88-8-88000-2000022-2-222-20000i10−i10−i10i10−i10i10i10−i1000000000000000000000000000000000000
χ668-88-8-88000-2000022-2-222-20000−i10i10i10−i10i10−i10−i10i1000000000000000000000000000000000000
χ678-8-88008-80-2000025−2525−25-222-2−252520000000000000000000000000000000000000000000
χ688-8-88008-80-20000−2525−2525-222-225−2520000000000000000000000000000000000000000000

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