Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C11 ⋊ #2296 |
656 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 285 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=g,b^2=g,d^2=f,b^a=be,c^a=cf,h^a=h^10376 conjugacy classes — view the full character table.
| maximal subgroup of | #14641727, #14641788, #14641791, … |
| maximal normal subgroup of | #14641727, #14641788, #14641791, … |
| maximal quotient of | #14674889, #14674904, C4×#10622823, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6993);