Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C19 · Schur multiplier (H2) = C2 |
| direct product | C2×C19×(C13⋊C3)⋊D13 |
| unambiguous semidirect product | (C2×C13⋊C3)⋊(C19×D13) |
| Fitting, socle | C2×C132×C19 ⋊ C2×C3 |
| derived, Sylow | C132 ⋊ C22×C3×C19 |
| Hall | C2×C19×C13⋊D13 ⋊ C3 |
| Hall | C13×C19×C13⋊C3 ⋊ C22 |
| Hall | C132×C19 ⋊ C22×C3 |
| Hall | C2×C13⋊D13 ⋊ C3×C19 |
| Hall | C13×C13⋊C3 ⋊ C22×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | (C13⋊C3)⋊D13 |
| commutator, cosocle, hypocenter | C132 | C22×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132×C19 | C2×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2×C19 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1482 |
1900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 313);