Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C11×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C11 ⋊ #2008 |
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,d^b=dg,h^b=h^10,d^c=dg,e^c=eg133 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2008, C2×#13069667, #14780778, … |
| maximal normal subgroup of | D11×#2008, C2×#13069667, #14780778, … |
| maximal quotient of | #14654079, #14654093, #14654107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5561);