Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24×C3 |
| direct product | C3⋊D3×#323 |
| Fitting | C32×#323 ⋊ C2 |
| Sylow | C32 ⋊ C2×#323 |
1368 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1368 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7716);