Finite Group DatabasebetaFinite Group Databasebeta| order | 3900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13049907⋊C3 |
| Fitting, derived, Hall | C13×C25 ⋊ C3×C4 |
| Hall | #13049907 ⋊ C3 |
| Hall | C25×C13⋊C3 ⋊ C4 |
| Hall | C13⋊C3 ⋊ #1035 |
| Sylow | C25 ⋊ AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C25 | C3×C4 |
| Frattini | C5 | #63121⋊C3 |
| socle | C5×C13 | C3×AGL(1,𝔽5) |
| prime radical | C25⋊(D13⋊C3) | C2 |
| cosocle | D325 | C2×C3 |
| LCS | G ▷ C13×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 325 |
Polycyclic presentation:
2,3,2,5,13,5|a^2=c,d^5=f^2,d^a=d^3f,e^a=e^5,f^a=f^3,e^b=e^3,d^c=d^4f^3,e^c=e^12,f^c=f^455 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3900, 17);