Finite Group DatabasebetaFinite Group Databasebeta| order | 19788 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | Dic17×C97⋊C3 |
| unambiguous semidirect product | (Dic17×C97)⋊C3 |
| derived, Hall | C17×C97 ⋊ C3×C4 |
| Hall | Dic17×C97 ⋊ C3 |
| Hall | C17×C97⋊C3 ⋊ C4 |
| Sylow | C97 ⋊ C3×Dic17 |
| Sylow | C17 ⋊ C4×C97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D17×C97⋊C3 |
| commutator, hypocenter | C17×C97 | C3×C4 |
| Fitting, socle, cosocle | C2×C17×C97 | C2×C3 |
| prime radical | C2×C17×C97⋊C3 | C2 |
| LCS | G ▷ C17×C97 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6596 |
700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19788, 11);