Finite Group DatabasebetaFinite Group Databasebeta| order | 3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | Dic3×AGL(1,𝔽17) |
| derived, Hall | C3×C17 ⋊ C4×C16 |
| Sylow | C17 ⋊ Dic3×C16 |
| Sylow | C3 ⋊ C4×AGL(1,𝔽17) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×AGL(1,𝔽17) |
| commutator, hypocenter | C3×C17 | C4×C16 |
| Fitting, socle | C2×C3×C17 | C2×C16 |
| prime radical | C2×C3×D17 | C2×C8 |
| cosocle | C2×C3×#3633 | C22 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2 | |
116 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 204 |
102 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.