Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#554 ⋊ C2 |
| Sylow | C11 ⋊ #3331 |
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^10154 conjugacy classes — view the full character table.
| maximal subgroup of | #14743406, #14743408, #14743466, … |
| maximal normal subgroup of | #14743406, #14743408, #14743466, … |
| maximal quotient of | #14769419, #14770222, #14771003, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16820);