Finite Group DatabasebetaFinite Group Databasebeta| order | 32416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D1013⋊C16 |
| derived, Sylow | C1013 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #16860990 |
| commutator, hypocenter | C1013 | C2×C16 |
| Frattini | C4 | C2×#16860990 |
| Fitting | C8×C1013 | C4 |
| socle | C2×C1013 | C2×C8 |
| prime radical | C2×D1013 | C8 |
| cosocle | #22549201 | C22 |
| LCS | G ▷ C1013 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16208 |
Polycyclic presentation:
2^5,1013|a^2=c,c^2=d,d^2=e,f^a=f^968,f^b=f^1012,f^c=f^10122056 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32416, 219);