Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C3 |
| direct product | H(5,𝔽2)×#157 |
| Fitting | C32×H(5,𝔽2) ⋊ C4 |
| Sylow | C32 ⋊ C4×H(5,𝔽2) |
2558 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 2558 conjugacy classes of subgroups — too many to draw. Only its 754 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | H(5,𝔽2)×PSU(3,𝔽2), H(5,𝔽2)×GO+(4,𝔽2), H(5,𝔽2)×AGL(1,𝔽9), … |
| maximal normal subgroup of | H(5,𝔽2)×PSU(3,𝔽2), H(5,𝔽2)×GO+(4,𝔽2), H(5,𝔽2)×AGL(1,𝔽9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134183);