Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C3×C42 |
| direct product | #97×#157 |
| Fitting | C32×#97 ⋊ C4 |
| Sylow | C32 ⋊ C4×#97 |
506 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #97×PSU(3,𝔽2), #97×GO+(4,𝔽2), #97×AGL(1,𝔽9) |
| maximal normal subgroup of | #97×PSU(3,𝔽2), #97×GO+(4,𝔽2), #97×AGL(1,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17036);