Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #1413 |
78 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=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cf,d^b=def,e^b=eg,h^b=h^10,d^c=dfg,e^d=eg79 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1413, C2×#13066788, #14674131, … |
| maximal normal subgroup of | D11×#1413, C2×#13066788, #14674131, … |
| maximal quotient of | #14641163, #14641181, #14641312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2682);