Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #1365 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=eg,c^2=fg,d^2=efg,f^2=g,b^a=bc,c^a=ce,h^a=h^10,c^b=cf,d^b=def,f^b=fg,h^b=h^10169 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1365, C2×#13066675, #14665057, … |
| maximal normal subgroup of | D11×#1365, C2×#13066675, #14665057, … |
| maximal quotient of | #14640565, #14640960, #14641434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2569);