Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×PSU(3,𝔽2)⋊C8 |
| Sylow | C32 ⋊ C2×Q8⋊C8 |
318 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(PSU(3,𝔽2)⋊C3)⋊C8, C2×C8×AΓL(1,𝔽9), #72244965, … |
| maximal normal subgroup of | C2×C8×AΓL(1,𝔽9), #72244965, #72252932, … |
| maximal quotient of | #72245163 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 8232);