Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C22×#64241 |
| Fitting | C24×C32 ⋊ D4 |
| Sylow | C32 ⋊ C22×#120 |
8050 conjugacy classes of subgroups; only the 583 normal subgroups are shown.
This group has 8050 conjugacy classes of subgroups — too many to draw. Only its 583 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
108 conjugacy classes — view the full character table.
| maximal quotient of | C2×#11864797 |
| automorphism group of | D32×C8, #63791, #63803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134274);