Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #1414 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=f,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^10,c^b=cfg,d^b=defg,e^b=eg,h^b=h^10,d^c=dfg,e^d=eg82 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1414, C2×#13066792, #14674144, … |
| maximal normal subgroup of | D11×#1414, C2×#13066792, #14674144, … |
| maximal quotient of | #14641165, #14641179, #14641311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2686);