Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#1780⋊C3 |
| unambiguous semidirect product | #1780⋊C32 |
| unambiguous semidirect product | (C3×#1780)⋊C3 |
| Fitting | C3×#1780 ⋊ C3 |
| Sylow | #1780 ⋊ C32 |
284 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153357);