Finite Group DatabasebetaFinite Group Databasebeta| order | 3756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#11929411 |
| Fitting, socle, Hall | C3×C313 ⋊ C4 |
| derived, Sylow | C313 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11929411 |
| commutator, hypocenter | C313 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C313 | C4 |
| prime radical | C3×D313 | C2 |
| cosocle | D313 | C2×C3 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 316 |
| transitive degree | μt(G) = 939 |
246 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3756, 10);