Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | Dic3×C9⋊C8 |
| derived, Sylow | C3×C9 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D3×D9 |
| commutator, hypocenter | C3×C9 | C4×C8 |
| Frattini | C2×C3×C4 | D32 |
| Fitting, cosocle | C2×C3×C4×C9 | C22 |
| socle, prime radical | C22×C32 | C2×Dic3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C2×C4 | |
154 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 79 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 | Dic6×C9⋊C8, #13137020, #13137021, … |
| maximal normal subgroup of | Dic6×C9⋊C8, #13137020, #13137021, … |
| maximal quotient of | C3⋊C8×C9⋊C8, #13134923, Dic3×C9⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 224);