Finite Group Databasebeta

← Group #13026293

Character table — Group #13026293

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1124444444444444558888888888888881016161616161616161620202020202020202040404040404040808080808080
order12222444444451010104424420202020202020202020202041010101020202020202222244444448888448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-1111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−i
χ41111111111111111-1-1111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii
χ511111111-1-1-1-1111111-11-1-1-1-1-11111-1-1-1-1111-1-111-1-1111-1-11-1-111-11-11111-1-11-11-1
χ611111111-1-1-1-1111111-11-1-1-1-1-11111-1-1-1-1111-1-111-1-1111-1-11-1-111-11-1-1-1-1-111-11-11
χ711111111-1-1-1-11111-1-1-11-1-1-1-1-11111-1-1-1-1-111-1-111-1-11-1-111-111-1-11-11ii−i−i−iii−i−ii
χ811111111-1-1-1-11111-1-1-11-1-1-1-1-11111-1-1-1-1-111-1-111-1-11-1-111-111-1-11-11−i−iiii−i−iii−i
χ9111111-1-111-1-1111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1111-1-111-1-111111-1-1-11-11
χ10111111-1-111-1-1111111-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1111-1-111-1-11-1-1-1-1111-11-1
χ11111111-1-111-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111-111-1-1-1-111111-1-1-111-1-111-1ii−i−i−ii−iii−i
χ12111111-1-111-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111-111-1-1-1-111111-1-1-111-1-111-1−i−iiii−ii−i−ii
χ13111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1111111-1-1111111-1-1-1-1
χ14111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ15111111-1-1-1-1111111-1-11-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-111ii−i−ii−i−i−iii
χ16111111-1-1-1-1111111-1-11-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-111−i−iii−iiii−i−i
χ172222-2-200220022222200-200000000222222-20000-2-2-20022-2002-200-20000000000
χ182222-2-20022002222-2-200-2000000002222-22-20000-2-2-200-2-2200-220020000000000
χ192222-2-200-2-20022222200200000000-2-2-2-222-2000022-200-2-2-2002-20020000000000
χ202222-2-200-2-2002222-2-200200000000-2-2-2-2-22-2000022-20022200-2200-20000000000
χ21222-22-22200002222220-200000222200002-2200-2-200-22200-200-220-200000000000
χ22222-22-22200002222-2-20-20000022220000-2-2200-2-200-2-2-2002002-20200000000000
χ23222-22-2-2-200002222220200000-2-2-2-200002-22002200-2-2-200-200-220200000000000
χ24222-22-2-2-200002222-2-20200000-2-2-2-20000-2-22002200-222002002-20-200000000000
χ25222-2-22000022222222-2002222000000002-2-2-2-2000020000222-2-2-2000000000000
χ26222-2-220000222222-2-2-200222200000000-2-2-2-2-2000020000-2-2-2222000000000000
χ27222-2-220000-2-2222222200-2-2-2-2000000002-2-2220000200002-2-2-2-22000000000000
χ28222-2-220000-2-22222-2-2200-2-2-2-200000000-2-2-222000020000-22222-2000000000000
χ29444444444444-1-1-1-100444-1-1-1-1-1-1-1-1-1-1-1-10-1-1-1-1-1-1-1-1-10000000000000000000000
χ3044444444-4-4-4-4-1-1-1-100-44-41111-1-1-1-111110-1-111-1-111-10000000000000000000000
χ31444444-4-444-4-4-1-1-1-100-4-4411111111-1-1-1-10-1-11111-1-1-10000000000000000000000
χ32444444-4-4-4-444-1-1-1-1004-4-4-1-1-1-1111111110-1-1-1-11111-10000000000000000000000
χ334444-4-4004400-1-1-1-10000-455−5−555−5−5-1-1-1-10-115−55−51110000000000000000000000
χ344444-4-4004400-1-1-1-10000-4−5−555−5−555-1-1-1-10-11−55−551110000000000000000000000
χ354444-4-400-4-400-1-1-1-10000455−5−5−5−55511110-115−5−55-1-110000000000000000000000
χ364444-4-400-4-400-1-1-1-100004−5−55555−5−511110-11−555−5-1-110000000000000000000000
χ37444-44-4440000-1-1-1-1000-4055−5−5-1-1-1-155−5−501-1−55115−510000000000000000000000
χ38444-44-4440000-1-1-1-1000-40−5−555-1-1-1-1−5−55501-15−511−5510000000000000000000000
χ39444-44-4-4-40000-1-1-1-10004055−5−51111−5−55501-1−55-1-1−5510000000000000000000000
χ40444-44-4-4-40000-1-1-1-100040−5−555111155−5−501-15−5-1-15−510000000000000000000000
χ41444-4-44000044-1-1-1-100-400-1-1-1-155−5−555−5−501111−55−55-10000000000000000000000
χ42444-4-44000044-1-1-1-100-400-1-1-1-1−5−555−5−555011115−55−5-10000000000000000000000
χ43444-4-440000-4-4-1-1-1-100400111155−5−5−5−555011-1-1−555−5-10000000000000000000000
χ44444-4-440000-4-4-1-1-1-1004001111−5−55555−5−5011-1-15−5−55-10000000000000000000000
χ4544-40000000004-4-4444000000000000000-40000000000000000000002-22-2000000
χ4644-40000000004-4-4444000000000000000-4000000000000000000000-22-22000000
χ4744-40000000004-4-44-4-400000000000000040000000000000000000002i−2i−2i2i000000
χ4844-40000000004-4-44-4-40000000000000004000000000000000000000−2i2i2i−2i000000
χ494-400002i−2i2i−2i2-2400-44i−4i0002-22-22i−2i2i−2i2i−2i2i−2i00000000002-22-202i−2i000000000000000
χ504-400002i−2i2i−2i2-2400-4−4i4i0002-22-22i−2i2i−2i2i−2i2i−2i0000000000-22-220−2i2i000000000000000
χ514-400002i−2i−2i2i-22400-44i−4i000-22-222i−2i2i−2i−2i2i−2i2i00000000002-2-220−2i2i000000000000000
χ524-400002i−2i−2i2i-22400-4−4i4i000-22-222i−2i2i−2i−2i2i−2i2i0000000000-222-202i−2i000000000000000
χ534-40000−2i2i2i−2i-22400-44i−4i000-22-22−2i2i−2i2i2i−2i2i−2i0000000000-222-20−2i2i000000000000000
χ544-40000−2i2i2i−2i-22400-4−4i4i000-22-22−2i2i−2i2i2i−2i2i−2i00000000002-2-2202i−2i000000000000000
χ554-40000−2i2i−2i2i2-2400-44i−4i0002-22-2−2i2i−2i2i−2i2i−2i2i0000000000-22-2202i−2i000000000000000
χ564-40000−2i2i−2i2i2-2400-4−4i4i0002-22-2−2i2i−2i2i−2i2i−2i2i00000000002-22-20−2i2i000000000000000
χ578-800004i−4i4i−4i4-4-225−25200000−1+51−5−1−51+5−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ700000000000000000000000000000000
χ588-800004i−4i4i−4i4-4-2−2525200000−1−51+5−1+51−5−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ1900000000000000000000000000000000
χ598-800004i−4i−4i4i-44-225−252000001−5−1+51+5−1−5−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ700000000000000000000000000000000
χ608-800004i−4i−4i4i-44-2−25252000001+5−1−51−5−1+5−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ1900000000000000000000000000000000
χ618-80000−4i4i4i−4i-44-225−252000001−5−1+51+5−1−52ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ700000000000000000000000000000000
χ628-80000−4i4i4i−4i-44-2−25252000001+5−1−51−5−1+52ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ1900000000000000000000000000000000
χ638-80000−4i4i−4i4i4-4-225−25200000−1+51−5−1−51+52ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ700000000000000000000000000000000
χ648-80000−4i4i−4i4i4-4-2−2525200000−1−51+5−1+51−52ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ1900000000000000000000000000000000
χ651616-16000000000-444-40000000000000000000000000000000000000000000000000

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