Finite Group DatabasebetaFinite Group Databasebeta| order | 1632 |
| isoclinism | isoclinic class of AGL(1,𝔽17) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C32 · Schur multiplier (H2) = C1 |
| direct product | C3×#10587664 |
| derived, Sylow | C17 ⋊ C3×C32 |
| Hall | C3×C17 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | AGL(1,𝔽17) |
| commutator, hypocenter | C17 | C3×C32 |
| Frattini | C2 | C3×AGL(1,𝔽17) |
| Fitting, socle, prime radical | C2×C3×C17 | C16 |
| cosocle | #63241 | C2×C3 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 52 |
| transitive degree | μt(G) = 1632 |
102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1632, 939);