Finite Group Databasebeta

← Group #13017691

Character table — Group #13017691

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111222244444444444888888888888888881010101016161616161616162020202020202020404040404040404040404080808080
order12222244224510101010101010444441010101020202020202020204444202020202020202022444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-111111111-1-1-1-1
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111iiii−i−i−i−i−i−iii
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111−i−i−i−iiiiiii−i−i
χ911111111-1-1111111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-111-1-111-1-11-11-1
χ1011111111-1-1111111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-111-1-111-11-11
χ1111111111-1-1111111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111ii−i−i−i−iiii−i−ii
χ1211111111-1-1111111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111−i−iiiii−i−i−iii−i
χ1311111111-1-1111111111-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-11111-1-111-1-1-11-11
χ1411111111-1-1111111111-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1111-11-1
χ1511111111-1-1111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-1ii−i−i−i−iii−iii−i
χ1611111111-1-1111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-1−i−iiiii−i−ii−i−ii
χ17222222-2-222-222222222-200002222-2-2-2-2-2-2-2-2222200000000220000-2-2-200000000000000
χ18222222-2-222-222222222-200002222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2000022200000000000000
χ19222222-2-2-2-2-22222222220000-2-2-2-2-2-2-2-22222222200000000-2-20000-2-2200000000000000
χ20222222-2-2-2-2-22222222220000-2-2-2-2-2-2-2-22222-2-2-2-20000000022000022-200000000000000
χ212222-2-22200-222-2-2-2-22202-200000022-2-200002-22-2000022-2-20022-2-22-2000000000000000
χ222222-2-22200-222-2-2-2-22202-200000022-2-20000-22-22000022-2-200-2-222-22000000000000000
χ232222-2-22200-222-2-2-2-2220-2200000022-2-200002-22-20000-2-22200-2-2222-2000000000000000
χ242222-2-22200-222-2-2-2-2220-2200000022-2-20000-22-220000-2-2220022-2-2-22000000000000000
χ252222-2-2-2-200222-2-2-2-2220002-20000-2-22200002-22-222-2-20000000000-2202-2000000000000
χ262222-2-2-2-200222-2-2-2-2220002-20000-2-2220000-22-2222-2-200000000002-20-22000000000000
χ272222-2-2-2-200222-2-2-2-222000-220000-2-22200002-22-2-2-2220000000000-220-22000000000000
χ282222-2-2-2-200222-2-2-2-222000-220000-2-2220000-22-22-2-22200000000002-202-2000000000000
χ2922-2-22-2002-202222-2-2-2-20000022-2-20000000022-2-2000000002-20000000002−22−22−22−20000
χ3022-2-22-2002-202222-2-2-2-20000022-2-20000000022-2-2000000002-2000000000−22−22−22−220000
χ3122-2-22-2002-202222-2-2-2-20000022-2-200000000-2-22200000000-22000000000i2−i2i2−i2−i2i2−i2i20000
χ3222-2-22-2002-202222-2-2-2-20000022-2-200000000-2-22200000000-22000000000−i2i2−i2i2i2−i2i2−i20000
χ3322-2-22-200-2202222-2-2-2-200000-2-2220000000022-2-200000000-220000000002−2−222−2−220000
χ3422-2-22-200-2202222-2-2-2-200000-2-2220000000022-2-200000000-22000000000−222−2−222−20000
χ3522-2-22-200-2202222-2-2-2-200000-2-22200000000-2-222000000002-2000000000i2−i2−i2i2−i2i2i2−i20000
χ3622-2-22-200-2202222-2-2-2-200000-2-22200000000-2-222000000002-2000000000−i2i2i2−i2i2−i2−i2i20000
χ3744444444444-1-1-1-1-1-1-1-144444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000000
χ3844444444444-1-1-1-1-1-1-1-14-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000000
χ3944444444-4-44-1-1-1-1-1-1-1-1-444-4-41111-1-1-1-1111100001111-1-1-1-100000000000000000000000
χ4044444444-4-44-1-1-1-1-1-1-1-1-4-4-4441111-1-1-1-111110000-1-1-1-1111100000000000000000000000
χ41444444-4-444-4-1-1-1-1-1-1-1-1-40000-1-1-1-11111111100005−55−55−55−500000000000000000000000
χ42444444-4-444-4-1-1-1-1-1-1-1-1-40000-1-1-1-1111111110000−55−55−55−5500000000000000000000000
χ43444444-4-4-4-4-4-1-1-1-1-1-1-1-14000011111111-1-1-1-100005−55−5−55−5500000000000000000000000
χ44444444-4-4-4-4-4-1-1-1-1-1-1-1-14000011111111-1-1-1-10000−55−555−55−500000000000000000000000
χ454444-4-44400-4-1-11111-1-104-4005−55−5-1-11155−5−500005−5−55-1-11100000000000000000000000
χ464444-4-44400-4-1-11111-1-104-400−55−55-1-111−5−5550000−555−5-1-11100000000000000000000000
χ474444-4-44400-4-1-11111-1-10-44005−55−5-1-11155−5−50000−555−511-1-100000000000000000000000
χ484444-4-44400-4-1-11111-1-10-4400−55−55-1-111−5−55500005−5−5511-1-100000000000000000000000
χ494444-4-4-4-4004-1-11111-1-10004-45−55−511-1-1−5−5550000-1-1115−5−5500000000000000000000000
χ504444-4-4-4-4004-1-11111-1-10004-4−55−5511-1-155−5−50000-1-111−555−500000000000000000000000
χ514444-4-4-4-4004-1-11111-1-1000-445−55−511-1-1−5−555000011-1-1−555−500000000000000000000000
χ524444-4-4-4-4004-1-11111-1-1000-44−55−5511-1-155−5−5000011-1-15−5−5500000000000000000000000
χ5344-4-4-440000044-4-444-4-4000000000000000004-4-440000000000000000000000000000000
χ5444-4-4-440000044-4-444-4-400000000000000000-444-40000000000000000000000000000000
χ554-44-4004-40004-40000-440000000004-400000000000000000000004i−4i00000000000000000
χ564-44-4004-40004-40000-440000000004-40000000000000000000000−4i4i00000000000000000
χ574-44-400-440004-40000-44000000000-44000000000000000000004i−4i0000000000000000000
χ584-44-400-440004-40000-44000000000-4400000000000000000000−4i4i0000000000000000000
χ5988-8-88-8008-80-2-2-2-2222200000-2-2220000000000000000000000000000000000000000000
χ6088-8-88-800-880-2-2-2-222220000022-2-20000000000000000000000000000000000000000000
χ6188-8-8-8800000-2-222-2-2220000025−25−25250000000000000000000000000000000000000000000
χ6288-8-8-8800000-2-222-2-22200000−252525−250000000000000000000000000000000000000000000
χ638-88-8008-8000-2225−2525−252-2000000000-2225−25000000000000000000000000000000000000000
χ648-88-8008-8000-22−2525−25252-2000000000-22−2525000000000000000000000000000000000000000
χ658-88-800-88000-2225−2525−252-20000000002-2−2525000000000000000000000000000000000000000
χ668-88-800-88000-22−2525−25252-20000000002-225−25000000000000000000000000000000000000000
χ678-8-8800000008-800008-80000000000000000000000000000000000000000000000000000
χ688-8-880000000-2225−25−2525-220000000000000−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ3800000000000000000000000000000000000
χ698-8-880000000-2225−25−2525-2200000000000002ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ3800000000000000000000000000000000000
χ708-8-880000000-22−252525−25-2200000000000002ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ3800000000000000000000000000000000000
χ718-8-880000000-22−252525−25-220000000000000−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ3800000000000000000000000000000000000

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