Finite Group Databasebeta

← Group #13017547

Character table — Group #13017547

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444444448888888888810101010101010101616161616161616161616162020202020202020202040404040404040404080808080
order12222244445101010224441010202020202222444410101010202020202020202022444444442444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1iiii−i−i−i−i-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1−i−i−i−iiiii-1-1-1-1-1−i−iii−i−iii
χ5111111111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-11111111111-1-11-1-11111-1-1-1-1
χ6111111111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111
χ7111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i11-111ii−i−i−i−iii
χ8111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii11-111−i−iiiii−i−i
χ911111111-1-11111-111-1-111-1-1-1-111111111-1-1111111-1-1-1-1-1-111111111-1-1-111-1-1-1-11-11-1
χ1011111111-1-11111-111-1-111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-11
χ1111111111-1-11111-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111iiii−i−i−i−i111-1-1−i−iiii−i−ii
χ1211111111-1-11111-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−i−i−iiiii111-1-1ii−i−i−iii−i
χ1311111111-1-11111-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-11-11
χ1411111111-1-11111-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-111111-11-1
χ1511111111-1-11111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i-1-1111−i−iii−iii−i
χ1611111111-1-11111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiii-1-1111ii−i−ii−i−ii
χ17222222-2-2222222-200002222222222-2-2-2-2-2-20000-2-20000-2-2000000000020000000000
χ18222222-2-2222222-20000222222-2-2-2-22222-2-20000-2-20000220000000000-20000000000
χ19222222-2-2-2-222222000022-2-2-2-22222-2-2-2-2220000-2-20000220000000000-20000000000
χ20222222-2-2-2-222222000022-2-2-2-2-2-2-2-22222220000-2-20000-2-2000000000020000000000
χ212222-2-22-20022220002-2-2-200002-22-222-2-20000002-222-2-200000000002-200000000000
χ222222-2-22-20022220002-2-2-20000-22-22-2-2220000002-222-2-20000000000-2200000000000
χ232222-2-22-2002222000-22-2-200002-22-222-2-20000002-2-2-2220000000000-2200000000000
χ242222-2-22-2002222000-22-2-20000-22-22-2-2220000002-2-2-22200000000002-200000000000
χ252222-2-2-2200222202-200-2-200002-22-2-2-2220022-2-2-22000000000000000002-200000000
χ262222-2-2-2200222202-200-2-20000-22-2222-2-20022-2-2-2200000000000000000-2200000000
χ272222-2-2-220022220-2200-2-200002-22-2-2-22200-2-222-2200000000000000000-2200000000
χ282222-2-2-220022220-2200-2-20000-22-2222-2-200-2-222-22000000000000000002-200000000
χ2922-2-22-2002i−2i22-2-2000002-22i2i−2i−2i00002i−2i2i−2i0000000000002-21+i1+i−1−i−1−i1−i1−i−1+i−1+i000001−i−1+i1+i−1−i0000
χ3022-2-22-2002i−2i22-2-2000002-22i2i−2i−2i00002i−2i2i−2i0000000000002-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000−1+i1−i−1−i1+i0000
χ3122-2-22-2002i−2i22-2-2000002-22i2i−2i−2i0000−2i2i−2i2i000000000000-221−i1−i−1+i−1+i1+i1+i−1−i−1−i00000−1−i1+i−1+i1−i0000
χ3222-2-22-2002i−2i22-2-2000002-22i2i−2i−2i0000−2i2i−2i2i000000000000-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i000001+i−1−i1−i−1+i0000
χ3322-2-22-200−2i2i22-2-2000002-2−2i−2i2i2i00002i−2i2i−2i000000000000-221+i1+i−1−i−1−i1−i1−i−1+i−1+i00000−1+i1−i−1−i1+i0000
χ3422-2-22-200−2i2i22-2-2000002-2−2i−2i2i2i00002i−2i2i−2i000000000000-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i000001−i−1+i1+i−1−i0000
χ3522-2-22-200−2i2i22-2-2000002-2−2i−2i2i2i0000−2i2i−2i2i0000000000002-21−i1−i−1+i−1+i1+i1+i−1−i−1−i000001+i−1−i1−i−1+i0000
χ3622-2-22-200−2i2i22-2-2000002-2−2i−2i2i2i0000−2i2i−2i2i0000000000002-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000−1−i1+i−1+i1−i0000
χ374444444444-1-1-1-144444-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ384444444444-1-1-1-14-4-4-4-4-1-1-1-1-1-100000000-1-11111-1-1111100000000000000000000000
χ3944444444-4-4-1-1-1-1-444-4-4-1-111110000000011-1-1-1-1-1-1111100000000000000000000000
χ4044444444-4-4-1-1-1-1-4-4-444-1-1111100000000111111-1-1-1-1-1-100000000000000000000000
χ41444444-4-444-1-1-1-1-40000-1-1-1-1-1-100000000115−55−5115−55−500000000000000000000000
χ42444444-4-444-1-1-1-1-40000-1-1-1-1-1-10000000011−55−5511−55−5500000000000000000000000
χ43444444-4-4-4-4-1-1-1-140000-1-1111100000000-1-15−55−511−55−5500000000000000000000000
χ44444444-4-4-4-4-1-1-1-140000-1-1111100000000-1-1−55−55115−55−500000000000000000000000
χ454444-4-44-400-1-1-1-10004-4115−55−5000000005−55−5−55-11-1-11100000000000000000000000
χ464444-4-44-400-1-1-1-10004-411−55−5500000000−55−555−5-11-1-11100000000000000000000000
χ474444-4-44-400-1-1-1-1000-44115−55−5000000005−5−555−5-1111-1-100000000000000000000000
χ484444-4-44-400-1-1-1-1000-4411−55−5500000000−555−5−55-1111-1-100000000000000000000000
χ494444-4-4-4400-1-1-1-104-400115−55−500000000−55-1-1111-15−5−5500000000000000000000000
χ504444-4-4-4400-1-1-1-104-40011−55−55000000005−5-1-1111-1−555−500000000000000000000000
χ514444-4-4-4400-1-1-1-10-4400115−55−500000000−5511-1-11-1−555−500000000000000000000000
χ524444-4-4-4400-1-1-1-10-440011−55−55000000005−511-1-11-15−5−5500000000000000000000000
χ5344-4-4-44000044-4-400000-44000000004i−4i−4i4i00000000000000000000000000000000000
χ5444-4-4-44000044-4-400000-4400000000−4i4i4i−4i00000000000000000000000000000000000
χ554-44-40000004-44-40000000000040-400000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000
χ564-44-40000004-44-40000000000040-40000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000
χ574-44-40000004-44-400000000000-40400000000000000000002-22-2-22-220000000000000
χ584-44-40000004-44-400000000000-4040000000000000000000-22-222-22-20000000000000
χ594-4-440000004-4-4400000000000040-40000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000
χ604-4-440000004-4-4400000000000040-4000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000
χ614-4-440000004-4-44000000000000-4040000000000000000002-2-22-222-20000000000000
χ624-4-440000004-4-44000000000000-404000000000000000000-222-22-2-220000000000000
χ6388-8-88-8008i−8i-2-22200000-22−2i−2i2i2i0000000000000000000000000000000000000000000
χ6488-8-88-800−8i8i-2-22200000-222i2i−2i−2i0000000000000000000000000000000000000000000
χ6588-8-8-880000-2-222000002-22i5−2i5−2i52i50000000000000000000000000000000000000000000
χ6688-8-8-880000-2-222000002-2−2i52i52i5−2i50000000000000000000000000000000000000000000
χ6716-1616-16000000-44-44000000000000000000000000000000000000000000000000000000
χ6816-16-1616000000-444-4000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).