Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| Fitting, socle, Sylow | C33 ⋊ C2×SD16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C3×#157 | C23 |
| Fitting, socle, hypocenter | C33 | C2×SD16 |
| prime radical | D3×GO+(4,𝔽2) | C2 |
| LCS | G ▷ C3×#157 ▷ C3×C3⋊D3 ▷ C33 | |
| UCS | C1 | |
178 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
27 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4662);