Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×SL(2,ℤ/4)⋊C8 |
| unambiguous semidirect product | SL(2,ℤ/4)⋊(C3×C8) |
348 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154896);