Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊#857 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C4×C3⋊#857 |
| Fitting | C3×C43 ⋊ D3 |
| derived | C3×C42⋊C3 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊#857 |
| commutator, hypocenter | C3×C42⋊C3 | C2×C4 |
| Frattini | C23 | C2×C3⋊S4 |
| Fitting | C3×C43 | D3 |
| socle | C23×C3 | C2×S4 |
| prime radical | C2×C3⋊#857 | C2 |
| cosocle | C2×C3×C42⋊C3 | C22 |
| LCS | G ▷ C3×C42⋊C3 | |
| UCS | C1 ◁ C4 | |
376 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154948);