Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#472 ⋊ C2 |
| Sylow | C11 ⋊ #3290 |
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,c^b=cg,d^b=de,e^b=eg,f^c=fg,h^c=h^10,e^d=eg,h^d=h^10109 conjugacy classes — view the full character table.
| maximal subgroup of | #14910517, #14910526, #14910537, … |
| maximal normal subgroup of | #14910517, #14910526, #14910537, … |
| maximal quotient of | #14745035, #14745078, #14745109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16291);