Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #1353 |
116 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=e,c^2=fg,d^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^10,c^b=cf,d^b=defg,d^c=dg133 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1353, C2×#13066643, #14664076, … |
| maximal normal subgroup of | D11×#1353, C2×#13066643, #14664076, … |
| maximal quotient of | #14640567, #14640593, #14640895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2537);