Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of AGL(1,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C3×#1057⋊C3 |
| unambiguous semidirect product | #1057⋊C32 |
| unambiguous semidirect product | (C3×#1057)⋊C3 |
| derived, Sylow | C13 ⋊ C32×C8 |
| Hall | C3×C13⋊C3 ⋊ C8 |
| Hall | #1057 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | AGL(1,𝔽13) |
| commutator, hypocenter | C13 | C32×C8 |
| Frattini | C2 | C3×AGL(1,𝔽13) |
| Fitting, socle | C2×C3×C13 | C3×C4 |
| prime radical | C2×C3×C13⋊C3 | C4 |
| cosocle | Dic13 | C2×C32 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1057⋊C3, #10597691⋊C3, #10597692⋊C3, … |
| maximal normal subgroup of | D3×#1057⋊C3, #10597691⋊C3, #10597692⋊C3, … |
| maximal quotient of | C3×#6092⋊C3, C2×C3×#1057⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 72);