Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C3 |
| direct product | C2×#10596547 |
| Fitting | C2×C32×Q8 ⋊ Q8 |
| Sylow | C32 ⋊ C2×#557 |
1126 conjugacy classes of subgroups; only the 463 normal subgroups are shown.
This group has 1126 conjugacy classes of subgroups — too many to draw. Only its 463 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 137722);