Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C3 |
| direct product | C2×#10596550 |
| Fitting | C24×C32 ⋊ Q8 |
| Sylow | C32 ⋊ C2×#543 |
1670 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 1670 conjugacy classes of subgroups — too many to draw. Only its 455 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 135888);