Finite Group DatabasebetaFinite Group Databasebeta| order | 19698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3283 |
| Fitting, Hall | C3×C49×C67 ⋊ C2 |
| derived, Hall | C49×C67 ⋊ C2×C3 |
| Hall | C3×C67 ⋊ D49 |
| Hall | C3×C49 ⋊ D67 |
| Sylow | C67 ⋊ C3×D49 |
| Sylow | C49 ⋊ C3×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3283 |
| commutator, cosocle, hypocenter | C49×C67 | C2×C3 |
| Frattini | C7 | C3×D469 |
| Fitting | C3×C49×C67 | C2 |
| socle | C3×C7×C67 | D7 |
| LCS | G ▷ C49×C67 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9849 |
4929 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19698, 8);