Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C22 |
| direct product | C2×#396⋊C9 |
| unambiguous semidirect product | (C2×#396)⋊C9 |
| derived | #95 ⋊ C22×C9 |
| Sylow | C2×#396 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #126⋊C3 |
| commutator, hypocenter | #95 | C22×C9 |
| Frattini | C23×C3 | C22×A4 |
| Fitting | C2×C3×#396 | C3 |
| socle | C24×C3 | C2×A4 |
| prime radical | C25×C3 | A4 |
| cosocle | C3×#95 | C22×C3 |
| LCS | G ▷ #95 | |
| UCS | C1 ◁ C22×C3 | |
389 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 389 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153452);