Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #2103 |
148 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 57 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=de,c^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^10,c^b=cf,d^b=dg,e^b=eg,f^b=fg166 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2103, C2×#13070198, #14783754, … |
| maximal normal subgroup of | D11×#2103, C2×#13070198, #14783754, … |
| maximal quotient of | #14658900, #14658905, #14658910, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6092);