Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #2231 |
120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=df,b^2=dg,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,h^b=h^10,e^c=efg,f^c=fg103 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2231, C2×#13070790, #14908511, … |
| maximal normal subgroup of | D11×#2231, C2×#13070790, #14908511, … |
| maximal quotient of | #14669877, #14670468, #14670472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6684);