Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C53 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×C3×C53×C19⋊C3 |
| Fitting, socle | C22×C3×C19×C53 ⋊ C3 |
| derived, Sylow | C19 ⋊ C22×C32×C53 |
| Hall | C22×C19×C53 ⋊ C32 |
| Hall | C19×C53 ⋊ C22×C32 |
| Hall | C22×C19 ⋊ C32×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C53 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C22×C32×C53 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C19×C53 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C22×C3×C53 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12084 |
5724 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 130);