Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10587628 |
| Fitting | C22×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | #14529150, #14529156, #14529254, … |
| maximal normal subgroup of | #14529150, #14529156, #14529254, … |
| maximal quotient of | C2×#11762818, C2×#11762808, C2×#11762849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1342);