Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#10588153 |
| Fitting | C2×C9×#100 ⋊ C2 |
| Sylow | C9 ⋊ C2×AΣL(1,𝔽16) |
657 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 657 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 30149);