Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×GO+(4,𝔽2)⋊C4 |
| unambiguous semidirect product | GO+(4,𝔽2)⋊(C22×C4) |
| Sylow | C32 ⋊ C22×#102 |
1446 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 1446 conjugacy classes of subgroups — too many to draw. Only its 236 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91749);