Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×#857⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | D3×#857⋊C2 |
| unambiguous semidirect product | (#857⋊D3)⋊C2 |
| unambiguous semidirect product | (D3×#857)⋊C2 |
| Fitting | C3×#127 ⋊ C2×D3 |
| derived | C3×C42⋊C3 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C42⋊C3 | C23 |
| Frattini | C22 | C2×D3×S4 |
| Fitting | C3×#127 | C2×D3 |
| socle | C22×C3 | C22×S4 |
| LCS | G ▷ C3×C42⋊C3 | |
| UCS | C1 | |
799 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 799 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) = 36 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#11715753, D3×#4626⋊C2, S4×#857⋊C2 |
| maximal normal subgroup of | D3×#4626⋊C2 |
| maximal quotient of | S4×#857⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155791);