Finite Group DatabasebetaFinite Group Databasebeta| order | 32896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×#16861595 |
| Fitting | C2×C4×Q8×C257 ⋊ C2 |
| Sylow | C257 ⋊ Q8×C22⋊C4 |
820 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 16448 |
5170 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32896, 7343);