Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D9×#237 |
| Fitting | C3×D4×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D3×D9 |
| commutator, cosocle | C2×C3×C9 | C24 |
| Frattini | C2×C3 | C22×D32 |
| Fitting | C3×D4×C9 | C22 |
| socle | C2×C32 | C23×D3 |
| hypercenter | D4 | D3×D9 |
| hypocenter | C3×C9 | C2×#41 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C2 ◁ D4 | |
532 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#911, D9×#912, #13149900, … |
| maximal normal subgroup of | D9×#911, D9×#912, #13149900, … |
| maximal quotient of | #13147937, #13147940, #13147945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2464);