Finite Group DatabasebetaFinite Group Databasebeta| order | 3512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D439 |
| Fitting | C22×C439 ⋊ C2 |
| Sylow | C439 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D439 |
| commutator, socle, cosocle | C2×C439 | C22 |
| Fitting | C22×C439 | C2 |
| hypercenter | C22 | D439 |
| hypocenter | C439 | D4 |
| LCS | G ▷ C2×C439 ▷ C439 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 443 |
| transitive degree | μt(G) = 1756 |
Polycyclic presentation:
2^3,439|b^a=bc,d^b=d^438881 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3512, 9);