Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #857⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C2×C3×#857⋊C2 |
| unambiguous semidirect product | #857⋊(C22×C3) |
| Fitting | C2×C3×#127 ⋊ D3 |
| derived | C42⋊C3 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #857⋊C2 |
| commutator, cosocle, hypocenter | C42⋊C3 | C23×C3 |
| Frattini | C22 | C22×C3×S4 |
| Fitting | C2×C3×#127 | D3 |
| socle | C23×C3 | C2×S4 |
| LCS | G ▷ C42⋊C3 | |
| UCS | C1 ◁ C2×C3 | |
799 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 799 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#4626⋊C2, C2×C3×#11715753 |
| maximal normal subgroup of | C2×C3×#4626⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156668);