Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | SL(2,𝔽3)×C13⋊C3 |
| unambiguous semidirect product | (Q8×C13⋊C3)⋊C3 |
| unambiguous semidirect product | (C13×SL(2,𝔽3))⋊C3 |
| unambiguous semidirect product | (Q8⋊(C13⋊C3))⋊C3 |
| Fitting, derived, Hall | Q8×C13 ⋊ C32 |
| Sylow | C13 ⋊ C3×SL(2,𝔽3) |
| Sylow | Q8 ⋊ C3×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×C13⋊C3 |
| commutator, Fitting, cosocle, hypocenter | Q8×C13 | C32 |
| socle | C2×C13 | C3×A4 |
| LCS | G ▷ Q8×C13 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
49 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×#226, C13⋊C3×GL(2,𝔽3), (C13⋊C3)⋊#226, … |
| maximal normal subgroup of | C13⋊C3×#226, C13⋊C3×GL(2,𝔽3), (C13⋊C3)⋊#226, … |
| maximal quotient of | C2×SL(2,𝔽3)×C13⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 81);