Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊#1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C4×C3⋊#1020 |
| Fitting | C24×C3×C4 ⋊ D3 |
| derived | C3×C22⋊A4 ⋊ C2×C4 |
956 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 956 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157779);