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 ⋊ #3361 |
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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=g,b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^10,d^b=de,f^c=fg160 conjugacy classes — view the full character table.
| maximal subgroup of | #14743623, #14743630, #14743758, … |
| maximal normal subgroup of | #14743623, #14743630, #14743758, … |
| maximal quotient of | #14770369, #14770583, #14772714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17170);