Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #1815 |
264 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^10,e^c=eg,f^c=fg232 conjugacy classes — view the full character table.
| maximal subgroup of | #14669525, #14669527, #14669932, … |
| maximal normal subgroup of | #14669525, #14669527, #14669932, … |
| maximal quotient of | #14646647, #14646662, #14646745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4569);