Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C9⋊#226 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C9⋊#226 |
| unambiguous semidirect product | (C2×C9)⋊#226 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C9⋊S4 |
| commutator, cosocle, hypocenter | C9×SL(2,𝔽3) | C22 |
| Frattini | C2×C3 | C2×C3⋊S4 |
| Fitting | C2×Q8×C9 | D3 |
| socle | C22×C3 | C3⋊S4 |
| prime radical | C2×C3×SL(2,𝔽3) | D3 |
| LCS | G ▷ C9×SL(2,𝔽3) | |
| UCS | C1 ◁ C22 | |
169 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 169 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #13146207, #13146210, #13146213, … |
| maximal normal subgroup of | #13146207, #13146210, #13146213, … |
| maximal quotient of | C4×C9⋊#226, C4⋊(C9⋊#226), #13146947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2336);