Finite Group DatabasebetaFinite Group Databasebeta| order | 1632 |
| isoclinism | isoclinic class of D3×#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D3×#63242 |
| derived, Hall | C3×C17 ⋊ C22×C8 |
| Sylow | C17 ⋊ C2×D3×C8 |
| Sylow | C3 ⋊ C2×#63242 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×#595 |
| commutator, hypocenter | C3×C17 | C22×C8 |
| Frattini | C2 | C2×D3×#595 |
| Fitting | C3×C4×C17 | C2×C4 |
| socle | C2×C3×C17 | C22×C4 |
| prime radical | C2×D3×D17 | C4 |
| cosocle | C3×Dic17 | C23 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C4 | |
152 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 408 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1632, 987);