Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #3386 |
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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=eg,b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^10,c^b=cg,d^b=de,f^c=fg154 conjugacy classes — view the full character table.
| maximal subgroup of | #14743251, #14743253, #14743296, … |
| maximal normal subgroup of | #14743251, #14743253, #14743296, … |
| maximal quotient of | #14770409, #14770416, #14772058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17431);