Finite Group DatabasebetaFinite Group Databasebeta| order | 19698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D67⋊C3 |
| unambiguous semidirect product | D67⋊(C3×C49) |
| unambiguous semidirect product | (C67⋊C3)⋊(C2×C49) |
| Fitting, Hall | C49×C67 ⋊ C2×C3 |
| derived, Sylow | C67 ⋊ C2×C3×C49 |
| Hall | C49×C67⋊C3 ⋊ C2 |
| Hall | C49×D67 ⋊ C3 |
| Hall | C67⋊C3 ⋊ C2×C49 |
| Hall | D67 ⋊ C3×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D67⋊C3 |
| commutator, hypocenter | C67 | C2×C3×C49 |
| Frattini | C7 | C7×D67⋊C3 |
| Fitting | C49×C67 | C2×C3 |
| socle, cosocle | C7×C67 | C2×C3×C7 |
| prime radical | C7×D67⋊C3 | C7 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3283 |
833 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19698, 13);