Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C3×#68049 |
| Fitting | C32×C82 ⋊ C2 |
| Sylow | C32 ⋊ #1454 |
393 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7682);