Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #1471 |
322 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=e,c^2=g,e^2=g,b^a=bd,d^a=df,h^a=h^10,c^b=cg,e^b=ef172 conjugacy classes — view the full character table.
| maximal subgroup of | #14645960, #14645962, #14645967, … |
| maximal normal subgroup of | #14645960, #14645962, #14645967, … |
| maximal quotient of | #14642150, #14642163, #14642177, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2870);