Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic1007 |
| derived, Hall | C19×C53 ⋊ C4×C9 |
| Hall | C9×C19×C53 ⋊ C4 |
| Hall | C9×C53 ⋊ Dic19 |
| Hall | C9×C19 ⋊ Dic53 |
| Sylow | C53 ⋊ C9×Dic19 |
| Sylow | C19 ⋊ C9×Dic53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D1007 |
| commutator, hypocenter | C19×C53 | C4×C9 |
| Frattini | C2×C3 | C3×D1007 |
| Fitting | C2×C9×C19×C53 | C2 |
| socle, prime radical, cosocle | C2×C3×C19×C53 | C2×C3 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 ◁ C2×C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36252 |
9090 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 5);