Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C19⋊C3×#6157 |
| unambiguous semidirect product | (C19×#6157)⋊C32 |
| unambiguous semidirect product | (C3×C19×#6157)⋊C3 |
| Fitting, socle | C3×C19×C53 ⋊ C3×C4 |
| derived, Hall | C19×C53 ⋊ C32×C4 |
| Hall | C3×C53×C19⋊C3 ⋊ C4 |
| Hall | C19×#6157 ⋊ C32 |
| Sylow | C53 ⋊ C3×C4×C19⋊C3 |
| Sylow | C19 ⋊ C32×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C19⋊C3×#6157 |
| commutator, hypocenter | C19×C53 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C53 | C3×C4 |
| prime radical | C3×C19⋊C3×D53 | C2 |
| cosocle | C19×D53 | C2×C32 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3021 |
459 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 74);