Finite Group DatabasebetaFinite Group Databasebeta| order | 19716 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C31⋊#6157 |
| Fitting, socle, Hall | C3×C31×C53 ⋊ C4 |
| derived, Hall | C31×C53 ⋊ C3×C4 |
| Hall | C3×C53 ⋊ Dic31 |
| Hall | C3×C31 ⋊ #6157 |
| Sylow | C53 ⋊ C3×Dic31 |
| Sylow | C31 ⋊ C3×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C31⋊#6157 |
| commutator, hypocenter | C31×C53 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C53 | C4 |
| prime radical | C3×C31×D53 | C2 |
| cosocle | C31×D53 | C2×C3 |
| LCS | G ▷ C31×C53 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4929 |
1311 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19716, 21);