Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C4 |
| direct product | C3⋊C8×C42⋊C3 |
| unambiguous semidirect product | C3⋊(C8×C42⋊C3) |
| unambiguous semidirect product | (C42×C3⋊C8)⋊C3 |
| derived | C3×C42 ⋊ C3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×C42⋊C3 |
| commutator, hypocenter | C3×C42 | C3×C8 |
| Frattini | C22×C4 | D3×A4 |
| Fitting, cosocle | C3×C43 | C2×C3 |
| socle | C23×C3 | C4×A4 |
| prime radical | C2×C3×C42⋊C3 | C4 |
| LCS | G ▷ C3×C42 | |
| UCS | C1 ◁ C4 | |
185 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 185 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154166);