Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×C4×#1020 |
| Fitting | C24×C3×C4 ⋊ D3 |
| derived | C22⋊A4 ⋊ C2×C3×C4 |
891 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 891 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157756);