Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C11×#500 ⋊ C2 |
| Sylow | C11 ⋊ #2240 |
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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|b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^a=h^10,h^b=h^10,h^c=h^10148 conjugacy classes — view the full character table.
| maximal subgroup of | #14667365, #14667366, #14667372, … |
| maximal normal subgroup of | #14667365, #14667366, #14667372, … |
| maximal quotient of | #14670152, #14671688, #14671986, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6735);