Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of D3×#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×#261 |
| Fitting, socle, Hall | C32×C13 ⋊ C2×C4 |
| derived | C3×C13 ⋊ C2×C3×C4 |
| Sylow | C13 ⋊ C3×C4×D3 |
| Sylow | C32 ⋊ C2×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×#261 |
| commutator, hypocenter | C3×C13 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13 | C2×C4 |
| prime radical | C3×D3×D13 | C2 |
| cosocle | C3×D13 | C22×C3 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C3 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 78 |
63 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#261, C2×C3×D3×#261, C3×D3×AGL(1,𝔽13), … |
| maximal normal subgroup of | D32×#261, C2×C3×D3×#261, C3×D3×AGL(1,𝔽13), … |
| maximal quotient of | C3×Dic3×#261, C3×(C2×D3)⋊#261, C3×Dic3⋊#261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 178);