Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊(C19⋊#6157) |
| unambiguous semidirect product | C3⋊(C3×C19⋊#6157) |
| Fitting, socle, Hall | C32×C19×C53 ⋊ C4 |
| derived | C3×C19×C53 ⋊ C3×C4 |
| Hall | C19×C53 ⋊ C3×Dic3 |
| Hall | C32×C53 ⋊ Dic19 |
| Hall | C32×C19 ⋊ #6157 |
| Sylow | C53 ⋊ C3×Dic57 |
| Sylow | C19 ⋊ C3×C3⋊#6157 |
| Sylow | C32 ⋊ C19⋊#6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C19⋊#6157) |
| commutator, hypocenter | C3×C19×C53 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C19×C53 | C4 |
| prime radical | C32×C19×D53 | C2 |
| cosocle | C3×C19×D53 | C2×C3 |
| LCS | G ▷ C3×C19×C53 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6042 |
2403 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 104);