Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #1409 |
110 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=g,c^2=fg,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cfg,d^b=def,e^b=eg,h^b=h^10,d^c=dfg,e^d=eg82 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1409, C2×#13066780, #14674082, … |
| maximal normal subgroup of | D11×#1409, C2×#13066780, #14674082, … |
| maximal quotient of | #14641157, #14641189, #14641282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2674);