Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×AGL(1,𝔽9) |
| Fitting | C22×C32×C4 ⋊ C8 |
| derived, Sylow | C32 ⋊ C22×C4×C8 |
878 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 407 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#10596408, C22×#72213199 |
| maximal normal subgroup of | C22×#10596408 |
| maximal quotient of | C22×#72213199 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91124);