Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C3 |
| direct product | C19×C3⋊Dic159 |
| unambiguous semidirect product | C3⋊(C19×Dic159) |
| derived, Hall | C32×C53 ⋊ C4×C19 |
| Hall | C32×C19×C53 ⋊ C4 |
| Hall | C19×C53 ⋊ C3⋊Dic3 |
| Hall | C32×C19 ⋊ Dic53 |
| Sylow | C53 ⋊ C19×C3⋊Dic3 |
| Sylow | C32 ⋊ C19×Dic53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | C3⋊D159 |
| commutator, hypocenter | C32×C53 | C4×C19 |
| Frattini | C2 | C19×C3⋊D159 |
| Fitting, socle, prime radical | C2×C32×C19×C53 | C2 |
| cosocle | C2×C32×C53 | C2×C19 |
| LCS | G ▷ C32×C53 | |
| UCS | C1 ◁ C2×C19 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36252 |
9120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 56);