Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×GO+(4,𝔽2) |
| unambiguous semidirect product | #157⋊(C2×C13) |
| unambiguous semidirect product | D32⋊(C2×C13) |
| Fitting, socle, Hall | C32×C13 ⋊ D4 |
| Sylow | C32 ⋊ D4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | GO+(4,𝔽2) |
| commutator, cosocle | C3⋊D3 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13 | D4 |
| hypocenter | C32 | D4×C13 |
| LCS | G ▷ C3⋊D3 ▷ C32 | |
| UCS | C1 ◁ C13 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 78 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C13×AΓL(1,𝔽9), #14273391, D13×GO+(4,𝔽2), … |
| maximal normal subgroup of | C13×AΓL(1,𝔽9), #14273391, D13×GO+(4,𝔽2), … |
| maximal quotient of | C13×D32⋊C4, C13×#3773, C13×#3774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 184);