Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C4×Dic3×C3⋊D3 |
| derived, Sylow | C33 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D3×C3⋊D3 |
| commutator, hypocenter | C33 | C2×C42 |
| Frattini | C22 | C2×D3×C3⋊D3 |
| Fitting | C2×C33×C4 | C22 |
| socle, cosocle | C22×C33 | C23 |
| prime radical | C22×C3×C3⋊D3 | C22 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2×C4 | |
768 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 196 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13154800, #13154804, Dic3×#3710, … |
| maximal normal subgroup of | #13154800, #13154804, Dic3×#3710, … |
| maximal quotient of | C4×C3⋊D3×C3⋊C8, C3⋊D3×#803, #13158909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3430);