Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C3 |
| direct product | #41×PSU(3,𝔽2) |
| Fitting | C32×#41 ⋊ Q8 |
| Sylow | C32 ⋊ Q8×#41 |
1150 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 455 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #41×PSU(3,𝔽2)⋊C3, AGL(1,ℤ/8)×PSU(3,𝔽2), #72220204, … |
| maximal normal subgroup of | #41×PSU(3,𝔽2)⋊C3, AGL(1,ℤ/8)×PSU(3,𝔽2), #72220204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 137808);