Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| direct product | C22×C13×#10625203 |
| Fitting, socle, Hall | C22×C132×C19 ⋊ C3 |
| derived | C13×C19 ⋊ C22×C3×C13 |
| Hall | C132×C19 ⋊ C22×C3 |
| Hall | C22×C132 ⋊ C19⋊C3 |
| Sylow | C132 ⋊ C22×C19⋊C3 |
| Hall | C22×C19 ⋊ C13×C13⋊C3 |
| Sylow | C19 ⋊ C22×C13×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C13 | #10625203 |
| commutator, cosocle, hypocenter | C13×C19 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C132×C19 | C3 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C22×C13 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2964 |
4420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 408);