Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×#10590153 |
| Fitting | C2×C32×C22⋊C4 ⋊ C4 |
| Sylow | C32 ⋊ C2×AΣL(1,𝔽16) |
1100 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 1100 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 30153);