Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #2583 |
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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=f,b^2=eg,c^2=g,b^a=be,c^a=cf,d^a=de,h^a=h^10,c^b=cg238 conjugacy classes — view the full character table.
| maximal subgroup of | #14651211, #14651213, #14651231, … |
| maximal normal subgroup of | #14651211, #14651213, #14651231, … |
| maximal quotient of | #14676168, #14676527, #14677477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 9890);