Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C257 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #14523348 |
| commutator, hypocenter | C257 | C2×C32 |
| Frattini | C4 | C2×#14523348 |
| Fitting | C8×C257 | C8 |
| socle | C2×C257 | C2×C16 |
| prime radical | C2×D257 | C16 |
| cosocle | #16861621 | C22 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C8 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8224 |
Polycyclic presentation:
2^6,257|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^64,g^b=g^256,g^c=g^241,g^d=g^256320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 1656);