Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of D9×#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D9×#261 |
| unambiguous semidirect product | (C9×#261)⋊C2 |
| unambiguous semidirect product | (C9⋊#261)⋊C2 |
| Fitting, derived, Hall | C9×C13 ⋊ C2×C4 |
| Sylow | C13 ⋊ C4×D9 |
| Sylow | C9 ⋊ C2×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C13 | C2×C4 |
| Frattini | C3 | D3×#261 |
| socle | C3×C13 | C4×D3 |
| prime radical | D9×D13 | C2 |
| cosocle | C9×D13 | C22 |
| LCS | G ▷ C9×C13 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 117 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D9×#261, D9×AGL(1,𝔽13), #261×AGL(1,ℤ/9), … |
| maximal normal subgroup of | C2×D9×#261, D9×AGL(1,𝔽13), #261×AGL(1,ℤ/9), … |
| maximal quotient of | D9×#1057, #14272507, #14272508, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 56);