Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | S4×#272 |
| Fitting | C22×H(3,𝔽3) ⋊ C2×D3 |
| derived | A4×H(3,𝔽3) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3⋊D3×S4 |
| commutator, cosocle, hypocenter | A4×H(3,𝔽3) | C22 |
| Fitting | C22×H(3,𝔽3) | C2×D3 |
| socle | C22×C3 | D3×C3⋊D3 |
| LCS | G ▷ A4×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
431 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2926);