Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C3×C4 |
| direct product | C42×C3⋊S4 |
| Fitting | C22×C3×C42 ⋊ D3 |
| derived | C3×A4 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | C3⋊S4 |
| commutator, hypocenter | C3×A4 | C2×C42 |
| Frattini | C22 | C22×C3⋊S4 |
| Fitting | C22×C3×C42 | D3 |
| socle | C24×C3 | C22×D3 |
| prime radical | C22×C3⋊S4 | C22 |
| cosocle | C22×C3×A4 | C23 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C42 | |
1210 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C42×A4⋊S4, #97×C3⋊S4 |
| maximal normal subgroup of | #97×C3⋊S4 |
| maximal quotient of | C42×A4⋊S4, #97×C3⋊S4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156846);