Finite Group DatabasebetaFinite Group Databasebeta| order | 4836 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C31 ⋊ C3×C4 |
| Hall | C31⋊#261 ⋊ C3 |
| Hall | #11925882 ⋊ C4 |
| Sylow | C31 ⋊ AGL(1,𝔽13) |
| Sylow | C13 ⋊ (C31⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C31 | C3×C4 |
| prime radical | #14559026 | C2 |
| cosocle | D13×C31 | C2×C3 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 403 |
Polycyclic presentation:
2,3,2,13,31|a^2=c,d^a=d^5,e^a=e^30,d^b=d^3,e^b=e^25,d^c=d^1253 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4836, 28);