Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of AGL(1,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#261⋊C9 |
| unambiguous semidirect product | #261⋊(C2×C9) |
| unambiguous semidirect product | (C2×#261)⋊C9 |
| unambiguous semidirect product | (D13⋊C9)⋊C4 |
| derived, Sylow | C13 ⋊ C2×C4×C9 |
| Hall | C13⋊C9 ⋊ C2×C4 |
| Hall | C2×#261 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | AGL(1,𝔽13) |
| commutator, hypocenter | C13 | C2×C4×C9 |
| Frattini | C3 | C2×AGL(1,𝔽13) |
| Fitting, socle | C2×C3×C13 | C3×C4 |
| prime radical | C2×C3×D13 | C2×C3 |
| cosocle | C3×D13 | C22×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 234 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#261⋊C9, C4⋊(#261⋊C9), (C22⋊#261)⋊C9, … |
| maximal normal subgroup of | C4×#261⋊C9, C4⋊(#261⋊C9), (C22⋊#261)⋊C9, … |
| maximal quotient of | (D13⋊C8)⋊C9, #6118⋊C9, C4×#261⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 55);