Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic13⋊C9 |
| unambiguous semidirect product | (C2×Dic13)⋊C9 |
| derived, Sylow | C13 ⋊ C2×C4×C9 |
| Hall | C13⋊C9 ⋊ C2×C4 |
| Hall | C2×Dic13 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D13⋊C3 |
| commutator, hypocenter | C13 | C2×C4×C9 |
| Frattini | C2×C3 | C2×D13⋊C3 |
| Fitting, socle, prime radical | C22×C3×C13 | C2×C3 |
| cosocle | C2×C3×C13 | C22×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 936 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Dic13⋊C9, #6101⋊C9, C4⋊(Dic13⋊C9), … |
| maximal normal subgroup of | C4×Dic13⋊C9, #6101⋊C9, C4⋊(Dic13⋊C9), … |
| maximal quotient of | C2×#1055⋊C9, #6099⋊C9, C4×Dic13⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 11);