Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C19⋊C3)⋊Dic53) |
| unambiguous semidirect product | (C19⋊C3)⋊Dic159 |
| unambiguous semidirect product | Dic3021⋊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 ⋊ C3⋊((C19⋊C3)⋊C4) |
| Sylow | C19 ⋊ C3×Dic159 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C53⋊(D19⋊C3)) |
| 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 |
Polycyclic presentation:
2,3^2,19,53,2|a^2=f,c^a=c^2,d^a=d^18,e^a=e^52,d^b=d^71440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 50);