Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#22576181 |
| Fitting | C2×SD16×C271 ⋊ C2 |
| Sylow | C271 ⋊ C2×#135 |
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8672 |
1918 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22576181, #46845159, #46845236, … |
| maximal normal subgroup of | C4×#22576181, #46845159, #46845236, … |
| maximal quotient of | C2×#31773890, C2×#31773892, C2×#31773932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 1330);