Finite Group DatabasebetaFinite Group Databasebeta| order | 16252 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic239⋊C17 |
| unambiguous semidirect product | (C239⋊C17)⋊C4 |
| derived, Sylow | C239 ⋊ C4×C17 |
| Hall | C239⋊C17 ⋊ C4 |
| Hall | Dic239 ⋊ C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D239⋊C17 |
| commutator, hypocenter | C239 | C4×C17 |
| Fitting, socle, cosocle | C2×C239 | C2×C17 |
| prime radical | C2×C239⋊C17 | C2 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 956 |
Polycyclic presentation:
2,17,239,2|a^2=d,c^a=c^238,c^b=c^21182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16252, 2);