Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C3×C42 |
| direct product | C2×#10596065 |
| Fitting | C2×C32×#120 ⋊ C2 |
| Sylow | C32 ⋊ C2×H(3,𝔽4) |
4224 conjugacy classes of subgroups; only the 793 normal subgroups are shown.
This group has 4224 conjugacy classes of subgroups — too many to draw. Only its 793 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 144219);