Finite Group DatabasebetaFinite Group Databasebeta| order | 29412 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| derived, Hall | C19×C43 ⋊ C32×C4 |
| Hall | C19⋊C3×C43⋊C3 ⋊ C4 |
| Hall | C19×Dic43 ⋊ C32 |
| Hall | Dic43 ⋊ C3×C19⋊C3 |
| Sylow | C43 ⋊ C3×C4×C19⋊C3 |
| Sylow | C19 ⋊ C3×(C43⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C19⋊C3×D43⋊C3 |
| commutator, hypocenter | C19×C43 | C32×C4 |
| Fitting, socle, cosocle | C2×C19×C43 | C2×C32 |
| prime radical | C2×C19⋊C3×C43⋊C3 | C2 |
| LCS | G ▷ C19×C43 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3268 |
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29412, 77);