Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×C4⋊(#126⋊C3) |
| unambiguous semidirect product | C4⋊(C3×#126⋊C3) |
| unambiguous semidirect product | #2860⋊C32 |
| unambiguous semidirect product | (C3×#2860)⋊C3 |
| Fitting | C3×#2860 ⋊ C3 |
| Sylow | #2860 ⋊ C32 |
300 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153519);