Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of A4×C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22×C33 |
| direct product | C2×A4×C3⋊(C3⋊D3) |
| unambiguous semidirect product | (C2×C3)⋊(A4×C3⋊D3) |
| Fitting, socle | C23×C33 ⋊ C2×C3 |
| derived | C22×C33 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×C3⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C22×C33 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C33 | C2×C3 |
| LCS | G ▷ C22×C33 | |
| UCS | C1 ◁ C2 | |
1404 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 1404 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3592);