Finite Group Databasebeta

← Group #13017592

Character table — Group #13017592

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111222244444444444888888888888888881010101016161616161616162020202020202020404040404040404040404080808080
order12222244444510101010101010444442020202020202020202020204444202020202020202022222244244444444448888
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
χ511111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111iiii−i−i−i−i−i−iii
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111−i−i−i−iiiiiii−i−i
χ911111111-1-1111111111-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-111-1-111-1-11-11-1
χ1011111111-1-1111111111-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-111-1-111-11-11
χ1111111111-1-1111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111ii−i−i−i−iiii−i−ii
χ1211111111-1-1111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111−i−iiiii−i−i−iii−i
χ1311111111-1-1111111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-11111-1-111-1-1-11-11
χ1411111111-1-1111111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-111-1-111-1-1111-11-1
χ1511111111-1-1111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111-1-1ii−i−i−i−iii−iii−i
χ1611111111-1-1111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111-1-1−i−iiiii−i−ii−i−ii
χ17222222-2-222-222222222-200002222-2-2-2-2-2-2-2-22222000000000000-2-222-200000000000000
χ18222222-2-222-222222222-200002222-2-2-2-2-2-2-2-2-2-2-2-200000000000022-2-2200000000000000
χ19222222-2-2-2-2-22222222220000-2-2-2-22222-2-2-2-22222000000000000-2-2-2-2200000000000000
χ20222222-2-2-2-2-22222222220000-2-2-2-22222-2-2-2-2-2-2-2-20000000000002222-200000000000000
χ212222-2-22200-22-2-2-2-222202-2000000000022-2-222-2-222-2-2000022-2-22-200000000000000000
χ222222-2-22200-22-2-2-2-222202-2000000000022-2-2-2-22222-2-20000-2-222-2200000000000000000
χ232222-2-22200-22-2-2-2-22220-22000000000022-2-222-2-2-2-2220000-2-2222-200000000000000000
χ242222-2-22200-22-2-2-2-22220-22000000000022-2-2-2-222-2-222000022-2-2-2200000000000000000
χ252222-2-2-2-20022-2-2-2-22220002-200000000-2-22222-2-2000022-2-20000-220002-2000000000000
χ262222-2-2-2-20022-2-2-2-22220002-200000000-2-222-2-222000022-2-200002-2000-22000000000000
χ272222-2-2-2-20022-2-2-2-2222000-2200000000-2-22222-2-20000-2-2220000-22000-22000000000000
χ282222-2-2-2-20022-2-2-2-2222000-2200000000-2-222-2-2220000-2-22200002-20002-2000000000000
χ292-22-22-2002-20222-2-22-2-20000022-2-2000000002i−2i2i−2i000000000000002i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ302-22-22-2002-20222-2-22-2-20000022-2-2000000002i−2i2i−2i000000000000002i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ312-22-22-2002-20222-2-22-2-20000022-2-200000000−2i2i−2i2i00000000000000−2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ322-22-22-2002-20222-2-22-2-20000022-2-200000000−2i2i−2i2i00000000000000−2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ332-22-22-200-220222-2-22-2-200000-2-222000000002i−2i2i−2i00000000000000−2i2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ342-22-22-200-220222-2-22-2-200000-2-222000000002i−2i2i−2i00000000000000−2i2i000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ352-22-22-200-220222-2-22-2-200000-2-22200000000−2i2i−2i2i000000000000002i−2i0001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ362-22-22-200-220222-2-22-2-200000-2-22200000000−2i2i−2i2i000000000000002i−2i000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
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
χ3944444444-4-44-1-1-1-1-1-1-1-1-444-4-411111111-1-1-1-10000-1-1-1-1111100000000000000000000000
χ4044444444-4-44-1-1-1-1-1-1-1-1-4-4-44411111111-1-1-1-100001111-1-1-1-100000000000000000000000
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
χ43444444-4-4-4-4-4-1-1-1-1-1-1-1-1400001111-1-1-1-1111100005−55−5−55−5500000000000000000000000
χ44444444-4-4-4-4-4-1-1-1-1-1-1-1-1400001111-1-1-1-111110000−55−555−55−500000000000000000000000
χ454444-4-44400-4-11111-1-1-104-4005−55−555−5−5-1-1110000-1-1115−5−5500000000000000000000000
χ464444-4-44400-4-11111-1-1-104-400−55−55−5−555-1-1110000-1-111−555−500000000000000000000000
χ474444-4-44400-4-11111-1-1-10-44005−55−555−5−5-1-111000011-1-1−555−500000000000000000000000
χ484444-4-44400-4-11111-1-1-10-4400−55−55−5−555-1-111000011-1-15−5−5500000000000000000000000
χ494444-4-4-4-4004-11111-1-1-10004-45−55−5−5−55511-1-100005−5−55-1-11100000000000000000000000
χ504444-4-4-4-4004-11111-1-1-10004-4−55−5555−5−511-1-10000−555−5-1-11100000000000000000000000
χ514444-4-4-4-4004-11111-1-1-1000-445−55−5−5−55511-1-10000−555−511-1-100000000000000000000000
χ524444-4-4-4-4004-11111-1-1-1000-44−55−5555−5−511-1-100005−5−5511-1-100000000000000000000000
χ534-44-4-44000004-4-4444-4-4000000000000000004i−4i−4i4i0000000000000000000000000000000
χ544-44-4-44000004-4-4444-4-400000000000000000−4i4i4i−4i0000000000000000000000000000000
χ554-4-44004-400040000-4-4400000000000004-400000000000000004-40000000000000000000
χ564-4-44004-400040000-4-4400000000000004-40000000000000000-440000000000000000000
χ574-4-4400-4400040000-4-440000000000000-44000000000000004-4000000000000000000000
χ584-4-4400-4400040000-4-440000000000000-4400000000000000-44000000000000000000000
χ5988-8-8000000080000-88-80000000000000000000000000000000000000000000000000000
χ6088-8-80000000-225−2525−252-22000000000−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18000000000000000000000000000000000000000
χ6188-8-80000000-225−2525−252-220000000002ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18000000000000000000000000000000000000000
χ6288-8-80000000-2−2525−25252-22000000000−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ18000000000000000000000000000000000000000
χ6388-8-80000000-2−2525−25252-220000000002ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18000000000000000000000000000000000000000
χ648-88-88-8008-80-2-2-222-22200000-2-2220000000000000000000000000000000000000000000
χ658-88-88-800-880-2-2-222-2220000022-2-20000000000000000000000000000000000000000000
χ668-88-8-8800000-222-2-2-2220000025−25−25250000000000000000000000000000000000000000000
χ678-88-8-8800000-222-2-2-22200000−252525−250000000000000000000000000000000000000000000
χ688-8-88008-8000-225−25−252522-20000000000000-2225−2500000000000000000000000000000000000
χ698-8-88008-8000-2−252525−2522-20000000000000-22−252500000000000000000000000000000000000
χ708-8-8800-88000-225−25−252522-200000000000002-2−252500000000000000000000000000000000000
χ718-8-8800-88000-2−252525−2522-200000000000002-225−2500000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.