Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #126⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C2×#383⋊C9 |
| unambiguous semidirect product | (C2×#383)⋊C9 |
| derived | C42 ⋊ C2×C4×C9 |
| Sylow | C2×#383 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #126⋊C3 |
| commutator, hypocenter | C42 | C2×C4×C9 |
| Frattini | C23×C3 | C22×A4 |
| Fitting | C2×C3×#383 | C3 |
| socle, prime radical | C24×C3 | C2×A4 |
| cosocle | C2×C3×C42 | C22×C3 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C22×C3 | |
264 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153420);