Finite Group DatabasebetaFinite Group Databasebeta| order | 29222 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D769 |
| unambiguous semidirect product | C769⋊(C2×C19) |
| Fitting, socle, Hall | C19×C769 ⋊ C2 |
| derived, Sylow | C769 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D769 |
| commutator, cosocle, hypocenter | C769 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C769 | C2 |
| LCS | G ▷ C769 | |
| UCS | C1 ◁ C19 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14611 |
7334 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29222, 2);