Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×C4×#994 |
| Fitting | C3×C4×H(5,𝔽2) ⋊ C3 |
| Sylow | C4×H(5,𝔽2) ⋊ C32 |
884 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153697);