Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C11×Q16 ⋊ C2 |
| Sylow | C11 ⋊ #3304 |
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=g,c^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^10,d^b=de,h^b=h^10,f^c=fg,h^d=h^10175 conjugacy classes — view the full character table.
| maximal subgroup of | #14743564, #14743572, #14743579, … |
| maximal normal subgroup of | #14743564, #14743572, #14743579, … |
| maximal quotient of | #14769244, #14770052, #14770985, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16451);