Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C53 · Schur multiplier (H2) = C2 |
| direct product | C2×C53×AGL(1,𝔽19) |
| unambiguous semidirect product | #4296⋊(C22×C53) |
| unambiguous semidirect product | (C2×#4296)⋊(C2×C53) |
| Fitting, socle | C2×C19×C53 ⋊ C2×C9 |
| derived, Sylow | C19 ⋊ C22×C9×C53 |
| Hall | C53×#4296 ⋊ C22 |
| Hall | C2×D19×C53 ⋊ C9 |
| Hall | C19×C53 ⋊ C22×C9 |
| Hall | #4296 ⋊ C22×C53 |
| Hall | C2×D19 ⋊ C9×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | AGL(1,𝔽19) |
| commutator, hypocenter | C19 | C22×C9×C53 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C53 | C2×C9 |
| prime radical | C2×C53×D19⋊C3 | C3 |
| cosocle | C19⋊C3 | C22×C3×C53 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C53 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2014 |
2014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 69);