Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×#11765850 |
| Fitting | D4×Q8×C71 ⋊ C2 |
| Sylow | C71 ⋊ Q8×D8 |
404 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
910 conjugacy classes — view the full character table.
| maximal subgroup of | #31986822, #31986823, #31986829, … |
| maximal normal subgroup of | #31986822, #31986823, #31986829, … |
| maximal quotient of | Q8×#14556048, Q8×#14556049, C4⋊C4×#11765850, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17361);