Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×#16861630 |
| derived, Sylow | C257 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #14523348 |
| commutator, hypocenter | C257 | C4×C16 |
| Frattini | C22 | C2×#14523348 |
| Fitting | C2×C4×C257 | C8 |
| socle, prime radical | C22×C257 | C2×C8 |
| cosocle | C2×#14523346 | C22 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C2×C4 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16448 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 1641);