Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #2072 |
238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=g,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,h^b=h^10,f^c=fg,h^c=h^10232 conjugacy classes — view the full character table.
| maximal subgroup of | #14642804, #14642805, #14642818, … |
| maximal normal subgroup of | #14642804, #14642805, #14642818, … |
| maximal quotient of | #14658485, #14658490, #14658502, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5920);