Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #857 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×C4×#857 |
| Fitting | C3×C43 ⋊ D3 |
| derived | C42⋊C3 ⋊ C2×C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | #857 |
| commutator, hypocenter | C42⋊C3 | C2×C3×C4 |
| Frattini | C23 | C2×C3×S4 |
| Fitting | C3×C43 | D3 |
| socle | C23×C3 | C2×S4 |
| prime radical | C2×C3×#857 | C2 |
| cosocle | C2×C42⋊C3 | C22×C3 |
| LCS | G ▷ C42⋊C3 | |
| UCS | C1 ◁ C3×C4 | |
337 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 337 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154770);