Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10587583 |
| Fitting | C2×C4⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
188 conjugacy classes — view the full character table.
| maximal subgroup of | #14529090, #14529095, #14529206, … |
| maximal normal subgroup of | #14529090, #14529095, #14529206, … |
| maximal quotient of | C2×#11762666, C2×#11762683, C2×#11762694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1048);