Finite Group Databasebeta

← Group #13017689

Character table — Group #13017689

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111222244444444444888888888888888881010101016161616161616162020202020202020404040404040404040404080808080
order12222244444510101010101010224442020202020202020202020204444101010102020202044444444444888888888888
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
χ51111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111111-1-1-1-1
χ61111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1-1-1-1-1-1-1-11111
χ71111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1iiii−i−i−i−i−i−iii
χ81111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1−i−i−i−iiiiiii−i−i
χ911111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-111-1-111-1-11-11-1
χ1011111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-111-1-111-11-11
χ1111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111ii−i−i−i−iiii−i−ii
χ1211111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111−i−iiiii−i−i−iii−i
χ1311111111-1-1111111111-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-111-1-111-1-1-11-11
χ1411111111-1-1111111111-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-111-1-1111-11-1
χ1511111111-1-1111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11ii−i−i−i−iii−iii−i
χ1611111111-1-1111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11−i−iiiii−i−ii−i−ii
χ17222222-2-222-2222222220000-22222-2-2-2-2-2-2-2-2222200000000220000-2-200-2000000000000
χ18222222-2-222-2222222220000-22222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2000022002000000000000
χ19222222-2-2-2-2-22222222200002-2-2-2-22222-2-2-2-2222200000000-2-20000-2-2002000000000000
χ20222222-2-2-2-2-22222222200002-2-2-2-22222-2-2-2-2-2-2-2-2000000002200002200-2000000000000
χ212222-2-22200-22-2-2-2-22222-20000000000022-2-22-22-222-2-200000022-2-22-2000000000000000
χ222222-2-22200-22-2-2-2-22222-20000000000022-2-2-22-2222-2-2000000-2-222-22000000000000000
χ232222-2-22200-22-2-2-2-2222-220000000000022-2-22-22-2-2-222000000-2-2222-2000000000000000
χ242222-2-22200-22-2-2-2-2222-220000000000022-2-2-22-22-2-22200000022-2-2-22000000000000000
χ252222-2-2-2-20022-2-2-2-2222002-2000000000-2-2222-22-2000022-2-2000000-222-20000000000000
χ262222-2-2-2-20022-2-2-2-2222002-2000000000-2-222-22-22000022-2-20000002-2-220000000000000
χ272222-2-2-2-20022-2-2-2-222200-22000000000-2-2222-22-20000-2-222000000-22-220000000000000
χ282222-2-2-2-20022-2-2-2-222200-22000000000-2-222-22-220000-2-2220000002-22-20000000000000
χ292-2-222-2002i−2i0222-2-22-2-2000002i2i−2i−2i000000002-2-22000000002i−2i000000000i2−i22−2i2−i22−20000
χ302-2-222-2002i−2i0222-2-22-2-2000002i2i−2i−2i000000002-2-22000000002i−2i000000000−i2i2−22−i2i2−220000
χ312-2-222-2002i−2i0222-2-22-2-2000002i2i−2i−2i00000000-222-200000000−2i2i0000000002−2−i2i2−22i2−i20000
χ322-2-222-2002i−2i0222-2-22-2-2000002i2i−2i−2i00000000-222-200000000−2i2i000000000−22i2−i22−2−i2i20000
χ332-2-222-200−2i2i0222-2-22-2-200000−2i−2i2i2i000000002-2-2200000000−2i2i000000000i2−i2−22i2−i2−220000
χ342-2-222-200−2i2i0222-2-22-2-200000−2i−2i2i2i000000002-2-2200000000−2i2i000000000−i2i22−2−i2i22−20000
χ352-2-222-200−2i2i0222-2-22-2-200000−2i−2i2i2i00000000-222-2000000002i−2i0000000002−2i2−i2−22−i2i20000
χ362-2-222-200−2i2i0222-2-22-2-200000−2i−2i2i2i00000000-222-2000000002i−2i000000000−22−i2i22−2i2−i20000
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
χ3844444444444-1-1-1-1-1-1-1-1-4-4-4-44-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000000
χ3944444444-4-44-1-1-1-1-1-1-1-144-4-4-411111111-1-1-1-10000-1-1-1-1111100000000000000000000000
χ4044444444-4-44-1-1-1-1-1-1-1-1-4-444-411111111-1-1-1-100001111-1-1-1-100000000000000000000000
χ41444444-4-444-4-1-1-1-1-1-1-1-10000-4-1-1-1-11111111100005−55−55−55−500000000000000000000000
χ42444444-4-444-4-1-1-1-1-1-1-1-10000-4-1-1-1-1111111110000−55−55−55−5500000000000000000000000
χ43444444-4-4-4-4-4-1-1-1-1-1-1-1-1000041111-1-1-1-1111100005−55−5−55−5500000000000000000000000
χ44444444-4-4-4-4-4-1-1-1-1-1-1-1-1000041111-1-1-1-111110000−55−555−55−500000000000000000000000
χ454444-4-44400-4-11111-1-1-14-40005−55−555−5−5-1-1110000-1-1115−5−5500000000000000000000000
χ464444-4-44400-4-11111-1-1-14-4000−55−55−5−555-1-1110000-1-111−555−500000000000000000000000
χ474444-4-44400-4-11111-1-1-1-440005−55−555−5−5-1-111000011-1-1−555−500000000000000000000000
χ484444-4-44400-4-11111-1-1-1-44000−55−55−5−555-1-111000011-1-15−5−5500000000000000000000000
χ494444-4-4-4-4004-11111-1-1-1004-405−55−5−5−55511-1-100005−5−55-1-11100000000000000000000000
χ504444-4-4-4-4004-11111-1-1-1004-40−55−5555−5−511-1-10000−555−5-1-11100000000000000000000000
χ514444-4-4-4-4004-11111-1-1-100-4405−55−5−5−55511-1-10000−555−511-1-100000000000000000000000
χ524444-4-4-4-4004-11111-1-1-100-440−55−5555−5−511-1-100005−5−5511-1-100000000000000000000000
χ534-44-4004-400040000-4-4400000000000004-40000000000000000004i−4i00000000000000000
χ544-44-4004-400040000-4-4400000000000004-4000000000000000000−4i4i00000000000000000
χ554-44-400-4400040000-4-440000000000000-4400000000000000004i−4i0000000000000000000
χ564-44-400-4400040000-4-440000000000000-440000000000000000−4i4i0000000000000000000
χ574-4-44-44000004-4-4444-4-40000000000000000044-4-40000000000000000000000000000000
χ584-4-44-44000004-4-4444-4-400000000000000000-4-4440000000000000000000000000000000
χ5988-8-8000000080000-88-80000000000000000000000000000000000000000000000000000
χ6088-8-80000000-225−2525−252-22000000000−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ38000000000000000000000000000000000000000
χ6188-8-80000000-225−2525−252-220000000002ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38000000000000000000000000000000000000000
χ6288-8-80000000-2−2525−25252-220000000002ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38000000000000000000000000000000000000000
χ6388-8-80000000-2−2525−25252-22000000000−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ38000000000000000000000000000000000000000
χ648-88-8008-8000-225−25−252522-20000000000000-2225−2500000000000000000000000000000000000
χ658-88-8008-8000-2−252525−2522-20000000000000-22−252500000000000000000000000000000000000
χ668-88-800-88000-225−25−252522-200000000000002-2−252500000000000000000000000000000000000
χ678-88-800-88000-2−252525−2522-200000000000002-225−2500000000000000000000000000000000000
χ688-8-888-8008i−8i0-2-2-222-22200000−2i−2i2i2i0000000000000000000000000000000000000000000
χ698-8-888-800−8i8i0-2-2-222-222000002i2i−2i−2i0000000000000000000000000000000000000000000
χ708-8-88-8800000-222-2-2-222000002i5−2i5−2i52i50000000000000000000000000000000000000000000
χ718-8-88-8800000-222-2-2-22200000−2i52i52i5−2i50000000000000000000000000000000000000000000

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