Finite Group DatabasebetaFinite Group Databasebeta| order | 3756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×C313⋊C3 |
| unambiguous semidirect product | (C4×C313)⋊C3 |
| Fitting, Hall | C4×C313 ⋊ C3 |
| derived, Sylow | C313 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C313⋊C3 |
| commutator, hypocenter | C313 | C3×C4 |
| Frattini | C2 | C2×C313⋊C3 |
| Fitting | C4×C313 | C3 |
| socle, cosocle | C2×C313 | C2×C3 |
| prime radical | C2×C313⋊C3 | C2 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 317 |
| transitive degree | μt(G) = 1252 |
428 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3×C313⋊C3, C3×C4×C313⋊C3, C4×C5×C313⋊C3, … |
| maximal normal subgroup of | C3×C4×C313⋊C3, C4×C5×C313⋊C3, C4×C7×C313⋊C3 |
| maximal quotient of | C4×C313⋊C9, Dic3×C313⋊C3, C3×C4×C313⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3756, 3);