Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C3×C8×Dic9 |
| derived | C9 ⋊ C3×C4×C8 |
| Sylow | C3×C9 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C8 | D9 |
| commutator, hypocenter | C9 | C3×C4×C8 |
| Frattini | C2×C3×C4 | C2×C3×D3 |
| Fitting | C2×C3×C8×C9 | C2 |
| socle, prime radical | C22×C32 | C4×D3 |
| cosocle | C2×C4×C9 | C22×C3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C3×C8 | |
154 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic9×C3⋊C16, Dic9⋊(C3⋊C16), #13135015, … |
| maximal normal subgroup of | Dic9×C3⋊C16, Dic9⋊(C3⋊C16), #13135015, … |
| maximal quotient of | C3×C8×C9⋊C8, C3×#10588131, C3×C16×Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 369);