Finite Group DatabasebetaFinite Group Databasebeta| order | 3756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic313 |
| derived, Sylow | C313 ⋊ C3×C4 |
| Hall | C3×C313 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D313 |
| commutator, hypocenter | C313 | C3×C4 |
| Frattini | C2 | C3×D313 |
| Fitting, socle, prime radical | C2×C3×C313 | C2 |
| cosocle | C2×C313 | C2×C3 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 320 |
| transitive degree | μt(G) = 3756 |
948 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic313⋊C9, C9×Dic313, C3×Dic313⋊C3, … |
| maximal normal subgroup of | Dic313⋊C9, C9×Dic313, C3×Dic313⋊C3, … |
| maximal quotient of | C9×Dic313, C32×Dic313, C3×Dic939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3756, 5);