Finite Group DatabasebetaFinite Group Databasebeta| order | 19836 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C19 · Schur multiplier (H2) = C3 |
| direct product | C32×C19×#1181 |
| Fitting, socle, Hall | C32×C19×C29 ⋊ C4 |
| derived, Sylow | C29 ⋊ C32×C4×C19 |
| Hall | C19×C29 ⋊ C32×C4 |
| Hall | C32×C29 ⋊ C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C19 | #1181 |
| commutator, hypocenter | C29 | C32×C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C19×C29 | C4 |
| prime radical | C32×C19×D29 | C2 |
| cosocle | D29 | C2×C32×C19 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C32×C19 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4959 |
1881 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19836, 93);