Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #63419 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#10588303 |
| derived | C42⋊C9 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #63419 |
| commutator, hypocenter | C42⋊C9 | C2×C4 |
| Frattini | C23×C3 | C2×S4 |
| Fitting | C22×C3×C42 | D3 |
| socle, prime radical | C24×C3 | S4 |
| cosocle | C2×C42⋊C9 | C22 |
| LCS | G ▷ C42⋊C9 | |
| UCS | C1 ◁ C22 | |
356 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154012);