Finite Group DatabasebetaFinite Group Databasebeta| order | 26999 |
| automorphism | ? |
| homology | Abelianization (H1) = C19×C49 · Schur multiplier (H2) = C1 |
| direct product | C19×C29⋊C49 |
| unambiguous semidirect product | C29⋊(C19×C49) |
| unambiguous semidirect product | (C19×C29)⋊C49 |
| derived, Sylow | C29 ⋊ C19×C49 |
| Hall | C19×C29 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C19 | C29⋊C7 |
| commutator, hypocenter | C29 | C19×C49 |
| Frattini | C7 | C19×C29⋊C7 |
| Fitting, socle, prime radical | C7×C19×C29 | C7 |
| cosocle | C7×C29 | C7×C19 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C7×C19 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26999 |
1463 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26999, 2);