Finite Group DatabasebetaFinite Group Databasebeta| order | 29244 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic2437⋊C3 |
| derived, Sylow | C2437 ⋊ C3×C4 |
| Hall | Dic2437 ⋊ C3 |
| Hall | C2437⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2437⋊C3 |
| commutator, hypocenter | C2437 | C3×C4 |
| Fitting, socle, cosocle | C2×C2437 | C2×C3 |
| prime radical | C2×C2437⋊C3 | C2 |
| LCS | G ▷ C2437 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9748 |
Polycyclic presentation:
2,3,2437,2|a^2=d,c^a=c^2436,c^b=c^2351824 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29244, 2);