Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D3×#338⋊C3 |
| unambiguous semidirect product | C3⋊(C2×#338⋊C3) |
| unambiguous semidirect product | (D3×#338)⋊C3 |
| Fitting, derived | C3×#338 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×C42⋊C3 |
| commutator, Fitting, cosocle, hypocenter | C3×#338 | C2×C3 |
| Frattini | C22×C4 | D3×A4 |
| socle | C2×C3 | C2×#95⋊C3 |
| LCS | G ▷ C3×#338 | |
| UCS | C1 ◁ C4 | |
191 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154162);