Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D13×D247 |
| Fitting, socle, Hall | C3×C132×C19 ⋊ C22 |
| derived, Hall | C132×C19 ⋊ C22×C3 |
| Hall | C3×C132 ⋊ C2×D19 |
| Sylow | C132 ⋊ C2×C3×D19 |
| Hall | C3×C19 ⋊ D132 |
| Sylow | C19 ⋊ C3×D132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D13×D247 |
| commutator, cosocle, hypocenter | C132×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132×C19 | C22 |
| LCS | G ▷ C132×C19 | |
| UCS | C1 ◁ C3 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1482 |
3000 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 362);