Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C24 |
| direct product | C3⋊C8×C22⋊A4 |
| unambiguous semidirect product | C3⋊(C8×C22⋊A4) |
| derived | C24×C3 ⋊ C3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×C22⋊A4 |
| commutator, hypocenter | C24×C3 | C3×C8 |
| Fitting, cosocle | C24×C3×C4 | C2×C3 |
| socle | C25×C3 | C3×C4 |
| prime radical | C2×C3×C22⋊A4 | C4 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C4 | |
773 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 773 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157442);