Finite Group DatabasebetaFinite Group Databasebeta| order | 32288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C1009 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #22549056 |
| commutator, hypocenter | C1009 | C2×C16 |
| Frattini | C2 | C2×#22549056 |
| Fitting | C4×C1009 | C8 |
| socle | C2×C1009 | C2×C8 |
| prime radical | C2×D1009 | C8 |
| cosocle | #22549054 | C22 |
| LCS | G ▷ C1009 | |
| UCS | C1 ◁ C4 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16144 |
Polycyclic presentation:
2^5,1009|a^2=c,c^2=d,d^2=e,f^a=f^762,f^b=f^1008,f^c=f^469,f^d=f^1008536 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32288, 241);