Finite Group DatabasebetaFinite Group Databasebeta| order | 22698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#26015440 |
| derived, Hall | C13×C97 ⋊ C2×C9 |
| Hall | C2×C13×C97 ⋊ C9 |
| Hall | C2×C97 ⋊ C13⋊C9 |
| Sylow | C97 ⋊ C2×C13⋊C9 |
| Hall | C2×C13 ⋊ C97⋊C9 |
| Sylow | C13 ⋊ C2×C97⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #16838253 |
| commutator, hypocenter | C13×C97 | C2×C9 |
| Frattini | C3 | C2×#16838253 |
| Fitting, socle, prime radical | C2×C3×C13×C97 | C3 |
| cosocle | C3×C13×C97 | C2×C3 |
| LCS | G ▷ C13×C97 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22698 |
2538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22698, 5);