Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C19⋊#6157 |
| Fitting, Hall | C9×C19×C53 ⋊ C4 |
| derived, Hall | C19×C53 ⋊ C4×C9 |
| Hall | C9×C53 ⋊ Dic19 |
| Hall | C9×C19 ⋊ #6157 |
| Sylow | C53 ⋊ C9×Dic19 |
| Sylow | C19 ⋊ C9×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C19⋊#6157 |
| commutator, hypocenter | C19×C53 | C4×C9 |
| Frattini | C3 | C3×C19⋊#6157 |
| Fitting | C9×C19×C53 | C4 |
| socle | C3×C19×C53 | C3×C4 |
| prime radical, cosocle | C3×C19×D53 | C2×C3 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9063 |
2421 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 21);