Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#10593414 |
| Fitting | C22×C32×C4 ⋊ D4 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
1798 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1798 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99277);