Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C11×#560 ⋊ C2 |
| Sylow | C11 ⋊ #2200 |
260 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 45 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|b^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^10,c^b=cg,e^b=efg,d^c=df,e^d=eg112 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2200, C2×#13070623, #14907821, … |
| maximal normal subgroup of | D11×#2200, C2×#13070623, #14907821, … |
| maximal quotient of | #14665820, #14665826, #14665854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6517);