Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C3 |
| direct product | C23×D3×C3⋊D3 |
| Fitting, socle | C23×C33 ⋊ C22 |
| derived, Sylow | C33 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×C3⋊D3 |
| commutator, cosocle, hypocenter | C33 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C23×C33 | C22 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C23 | |
5024 conjugacy classes of subgroups; only the 856 normal subgroups are shown.
This group has 5024 conjugacy classes of subgroups — too many to draw. Only its 856 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13156714, #13160877, #13166609, … |
| maximal normal subgroup of | #13156714, #13160877, #13166609, … |
| maximal quotient of | C22×C3⋊D3×Dic6, C22×#89021, C22×#89017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4718);