Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C32 · Schur multiplier (H2) = C1 |
| direct product | C3×C9⋊C32 |
| derived | C9 ⋊ C3×C32 |
| Sylow | C3×C9 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C16 | D9 |
| commutator, hypocenter | C9 | C3×C32 |
| Frattini | C3×C16 | C3×D3 |
| Fitting | C3×C9×C16 | C2 |
| socle, prime radical | C2×C32 | C3⋊C16 |
| cosocle | C9×C16 | C2×C3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C3×C16 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C3⋊D9)⋊C32, #13134894, D3×C9⋊C32, … |
| maximal normal subgroup of | (C3⋊D9)⋊C32, #13134894, D3×C9⋊C32, … |
| maximal quotient of | C3×C9⋊C64, C2×C3×C9⋊C32 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 64);