Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #1767 |
292 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=f,c^2=de,f^2=g,b^a=bd,c^b=cg,h^b=h^10376 conjugacy classes — view the full character table.
| maximal subgroup of | #14640315, #14640316, #14640329, … |
| maximal normal subgroup of | #14640315, #14640316, #14640329, … |
| maximal quotient of | #14644902, #14644912, #14644935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4363);