Finite Group DatabasebetaFinite Group Databasebeta| order | 22386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1599 |
| unambiguous semidirect product | C3⋊(C7×D533) |
| unambiguous semidirect product | C13⋊(C7×D123) |
| unambiguous semidirect product | C41⋊(C7×D39) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1599 |
| commutator, cosocle, hypocenter | C3×C13×C41 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C41 | C2 |
| LCS | G ▷ C3×C13×C41 | |
| UCS | C1 ◁ C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11193 |
5607 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22386, 16);