Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C11×#340 ⋊ C2 |
| Sylow | C11 ⋊ #1735 |
424 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 153 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=f,c^2=g,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^c=h^10196 conjugacy classes — view the full character table.
| maximal subgroup of | #14663998, #14664000, #14664008, … |
| maximal normal subgroup of | #14663998, #14664000, #14664008, … |
| maximal quotient of | #14643230, #14643240, #14643251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4225);