Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#63122 |
| Fitting | C4×C5×C13 ⋊ C4 |
| Hall | C5×C13 ⋊ C4⋊C4 |
| Sylow | C13 ⋊ C4⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#63122 |
| commutator, socle | C2×C5×C13 | C2×C4 |
| Fitting | C4×C5×C13 | C4 |
| prime radical, cosocle | C2×D65 | C22 |
| hypercenter | C4 | #63122 |
| hypocenter | C5×C13 | C4⋊C4 |
| LCS | G ▷ C2×C5×C13 ▷ C5×C13 | |
| UCS | C1 ◁ C2 ◁ C4 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 260 |
Polycyclic presentation:
2^4,5,13|a^2=c,b^2=d,b^a=bd,e^a=e^3,f^a=f^8,e^c=e^4,f^c=f^1274 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 130);