Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C9 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×C8×C22⋊C9 |
| unambiguous semidirect product | (C22×C4×C8)⋊C9 |
| derived | C22 ⋊ C4×C8×C9 |
| Sylow | C22×C4×C8 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4×C8 | A4 |
| commutator, hypocenter | C22 | C4×C8×C9 |
| Frattini | C2×C3×C4 | C22×A4 |
| Fitting | C22×C3×C4×C8 | C3 |
| socle, prime radical | C24×C3 | C2×C3×C4 |
| cosocle | C23×C3×C4 | C22×C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C4×C8 | |
356 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
384 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153528);