Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C3×C4×C22⋊A4 |
| Fitting | C25×C3×C4 ⋊ C3 |
| derived | C24 ⋊ C2×C32×C4 |
| Sylow | C25×C4 ⋊ C32 |
3816 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 3816 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153897);