Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×C3×C9⋊S4 |
| unambiguous semidirect product | (C2×A4)⋊(C3×D9) |
| Fitting | C23×C3×C9 ⋊ D3 |
| derived | C9×A4 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C9⋊S4 |
| commutator, cosocle, hypocenter | C9×A4 | C22×C3 |
| Frattini | C3 | C2×C3×C3⋊S4 |
| Fitting | C23×C3×C9 | D3 |
| socle | C23×C32 | C3⋊D3 |
| LCS | G ▷ C9×A4 | |
| UCS | C1 ◁ C2×C3 | |
346 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C9⋊#1020, C2×A4⋊(D27⋊C3), C3×C9⋊#5935, … |
| maximal quotient of | C2×C3×C9⋊#1020, C2×A4⋊(D27⋊C3), C2×C3×#11724027 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2994);