Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×PSU(3,𝔽2)⋊C4 |
| unambiguous semidirect product | PSU(3,𝔽2)⋊C42 |
| Sylow | C32 ⋊ C4×#103 |
386 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 100 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 | C4×(PSU(3,𝔽2)⋊C3)⋊C4, #72220415, C42×AΓL(1,𝔽9), … |
| maximal normal subgroup of | #72220415, C42×AΓL(1,𝔽9), #72220456, … |
| maximal quotient of | #72244965, #72252932 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 18002);