Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C271 ⋊ C2 |
| Sylow | C271 ⋊ #577 |
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4336 |
Polycyclic presentation:
2^6,271|a^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^270,e^b=ef,g^b=g^270,d^c=df2722 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46848127, #46848131, #46848138, … |
| maximal normal subgroup of | #46848127, #46848131, #46848138, … |
| maximal quotient of | #46844891, #46844898, #46844959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 1361);