Finite Group DatabasebetaFinite Group Databasebeta| order | 3756 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#11929411 |
| Fitting, socle, derived, Hall | C3×C313 ⋊ C4 |
| Sylow | C313 ⋊ Dic3 |
| Sylow | C3 ⋊ #11929411 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C313 | C4 |
| prime radical, cosocle | C3×D313 | C2 |
| LCS | G ▷ C3×C313 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 316 |
| transitive degree | μt(G) = 939 |
Polycyclic presentation:
2^2,3,313|a^2=b,c^a=c^2,d^a=d^288,d^b=d^312240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3756, 11);