Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#261×C19⋊C3 |
| Fitting, socle, Hall | C132×C19 ⋊ C3×C4 |
| derived | C13×C19 ⋊ C3×C4×C13 |
| Hall | C13×C19×#261 ⋊ C3 |
| Hall | C132×C19⋊C3 ⋊ C4 |
| Sylow | C132 ⋊ C4×C19⋊C3 |
| Sylow | C19 ⋊ C3×C13×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #261×C19⋊C3 |
| commutator, hypocenter | C13×C19 | C3×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C132×C19 | C3×C4 |
| prime radical | C13×D13×C19⋊C3 | C2 |
| cosocle | C19×D13 | C2×C3×C13 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C13 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 988 |
819 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 219);