Finite Group DatabasebetaFinite Group Databasebeta| order | 16252 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C239 ⋊ C2×C17 |
| derived, Sylow | C239 ⋊ C22×C17 |
| Hall | C239⋊C17 ⋊ C22 |
| Hall | C2×D239 ⋊ C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D239⋊C17 |
| commutator, cosocle, hypocenter | C239 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C239 | C2×C17 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 478 |
82 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16252, 8);