Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C11⋊#1308 |
| Sylow | C11 ⋊ #1308 |
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=e,d^2=fg,e^2=f,b^a=bc,c^a=cf,e^a=eg,c^b=cg,d^b=df,h^b=h^10166 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1308, C2×C11⋊#1308, #14644175, … |
| maximal normal subgroup of | D11×#1308, C2×C11⋊#1308, #14644175, … |
| maximal quotient of | #14640345, #14640346, #14640347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2422);