Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D53×#4296 |
| unambiguous semidirect product | C53⋊(C22×#4296) |
| unambiguous semidirect product | (C2×C53)⋊(C2×#4296) |
| Fitting, socle | C2×C19×C53 ⋊ C2×C9 |
| derived, Hall | C19×C53 ⋊ C22×C9 |
| Hall | C53×#4296 ⋊ C22 |
| Hall | C2×C19×D53 ⋊ C9 |
| Sylow | C53 ⋊ C22×#4296 |
| Sylow | C19 ⋊ C2×C9×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D53×#4296 |
| commutator, hypocenter | C19×C53 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C53 | C2×C9 |
| prime radical | C2×C19⋊C3×D53 | C3 |
| cosocle | C53×C19⋊C3 | C22×C3 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2014 |
616 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 71);