Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C2×C19×#11759813 |
| Fitting, socle | C2×C132×C19 ⋊ D3 |
| derived, Hall | #92789 ⋊ C22×C19 |
| Hall | C19×#92789 ⋊ C22 |
| Hall | C132×C19 ⋊ C2×D3 |
| Sylow | C132 ⋊ C2×D3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | #11759813 |
| commutator, cosocle, hypocenter | #92789 | C22×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132×C19 | D3 |
| LCS | G ▷ #92789 | |
| UCS | C1 ◁ C2×C19 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 988 |
1862 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 301);