Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×Dic159 |
| unambiguous semidirect product | C3⋊(C19⋊C3×Dic53) |
| unambiguous semidirect product | (C19×Dic159)⋊C3 |
| derived | C3×C19×C53 ⋊ C3×C4 |
| Hall | C3×C53×C19⋊C3 ⋊ C4 |
| Hall | C19×C53 ⋊ C3×Dic3 |
| Hall | C3×C19⋊C3 ⋊ Dic53 |
| Sylow | C53 ⋊ Dic3×C19⋊C3 |
| Sylow | C19 ⋊ C3×Dic159 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C19⋊C3×D159 |
| commutator, hypocenter | C3×C19×C53 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C19×C53 | C2×C3 |
| prime radical | C2×C3×C53×C19⋊C3 | C2 |
| LCS | G ▷ C3×C19×C53 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12084 |
1458 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 52);