Finite Group DatabasebetaFinite Group Databasebeta| order | 22698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3783 |
| unambiguous semidirect product | C3⋊(C3×D1261) |
| Fitting, socle, Hall | C32×C13×C97 ⋊ C2 |
| derived | C3×C13×C97 ⋊ C2×C3 |
| Hall | C13×C97 ⋊ C3×D3 |
| Hall | C32×C97 ⋊ D13 |
| Hall | C32×C13 ⋊ D97 |
| Sylow | C97 ⋊ C3×D39 |
| Sylow | C13 ⋊ C3×D291 |
| Sylow | C32 ⋊ D1261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3783 |
| commutator, cosocle, hypocenter | C3×C13×C97 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C97 | C2 |
| LCS | G ▷ C3×C13×C97 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7566 |
5679 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22698, 68);