Finite Group DatabasebetaFinite Group Databasebeta| order | 29412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#28413677 |
| Fitting, socle | C2×C19×C43 ⋊ C2×C9 |
| derived, Hall | C19×C43 ⋊ C22×C9 |
| Hall | #20301354 ⋊ C22 |
| Hall | C2×C19×D43 ⋊ C9 |
| Hall | C2×D43 ⋊ #4296 |
| Sylow | C43 ⋊ C22×#4296 |
| Sylow | C19 ⋊ C2×D43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #28413677 |
| commutator, hypocenter | C19×C43 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C43 | C2×C9 |
| prime radical | C2×C19⋊C3×D43 | C3 |
| cosocle | C43×C19⋊C3 | C22×C3 |
| LCS | G ▷ C19×C43 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1634 |
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29412, 137);