Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C53 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle, Hall | C22×C19×C53 ⋊ C32 |
| derived, Hall | C22×C19 ⋊ C32×C53 |
| Hall | C19×C53 ⋊ C3×A4 |
| Hall | C22×C53 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×A4×C53 |
| Sylow | C22 ⋊ C3×C53×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | A4×C19⋊C3 |
| commutator, cosocle, hypocenter | C22×C19 | C32×C53 |
| Frattini | C1 | G |
| Fitting, socle | C22×C19×C53 | C32 |
| LCS | G ▷ C22×C19 | |
| UCS | C1 ◁ C53 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4028 |
1908 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 84);