Finite Group DatabasebetaFinite Group Databasebeta| order | 21866 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×C29⋊D29 |
| unambiguous semidirect product | C29⋊(C13×D29) |
| Fitting, socle, Hall | C13×C292 ⋊ C2 |
| derived, Sylow | C292 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C29⋊D29 |
| commutator, cosocle, hypocenter | C292 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C292 | C2 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C13 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10933 |
5486 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21866, 7);