Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#22551693 |
| Fitting, socle | C2×C257 ⋊ C32 |
| derived, Sylow | C257 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22551693 |
| commutator, hypocenter | C257 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C257 | C32 |
| prime radical | C2×D257 | C16 |
| cosocle | #16861632 | C22 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C2 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 514 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 1683);