Finite Group DatabasebetaFinite Group Databasebeta| order | 21812 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic287 |
| unambiguous semidirect product | C7⋊(C19×Dic41) |
| derived, Hall | C7×C41 ⋊ C4×C19 |
| Hall | C7×C19×C41 ⋊ C4 |
| Hall | C19×C41 ⋊ Dic7 |
| Hall | C7×C19 ⋊ Dic41 |
| Sylow | C41 ⋊ C19×Dic7 |
| Sylow | C7 ⋊ C19×Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D287 |
| commutator, hypocenter | C7×C41 | C4×C19 |
| Frattini | C2 | C19×D287 |
| Fitting, socle, prime radical | C2×C7×C19×C41 | C2 |
| cosocle | C2×C7×C41 | C2×C19 |
| LCS | G ▷ C7×C41 | |
| UCS | C1 ◁ C2×C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21812 |
5510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21812, 6);