Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C11×#498 ⋊ C2 |
| Sylow | C11 ⋊ #3227 |
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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|b^2=e,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^10,c^b=ce,f^c=fg,h^d=h^10142 conjugacy classes — view the full character table.
| maximal subgroup of | #14732363, #14732399, #14732567, … |
| maximal normal subgroup of | #14732363, #14732399, #14732567, … |
| maximal quotient of | #14763257, #14763449, #14764286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15639);