Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of C3⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C2×C3 |
| direct product | C13×C3⋊S4 |
| unambiguous semidirect product | C3⋊(C13×S4) |
| unambiguous semidirect product | A4⋊(D3×C13) |
| Fitting, socle | C22×C3×C13 ⋊ D3 |
| derived | C3×A4 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C3⋊S4 |
| commutator, cosocle, hypocenter | C3×A4 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C13 | D3 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C13 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | D13×C3⋊S4, D3×C13×S4, (C3⋊S4)⋊D13, … |
| maximal normal subgroup of | D13×C3⋊S4, D3×C13×S4, (C3⋊S4)⋊D13, … |
| maximal quotient of | C13×C3⋊#226, C13×C3⋊GL(2,𝔽3), C13×C3⋊SL(2,ℤ/4), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 192);