Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #1684 |
144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 144 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) = 1408 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=dfg,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^10,e^c=eg,h^c=h^10169 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1684, C2×#13068075, #14736180, … |
| maximal normal subgroup of | D11×#1684, C2×#13068075, #14736180, … |
| maximal quotient of | #14646853, #14649918, #14649946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 3969);