Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #2043 |
298 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 91 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=g,b^2=g,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^10,c^b=cf,e^b=eg,f^b=fg,h^b=h^10,e^c=eg,f^c=fg,h^c=h^10232 conjugacy classes — view the full character table.
| maximal subgroup of | #14642631, #14642632, #14642638, … |
| maximal normal subgroup of | #14642631, #14642632, #14642638, … |
| maximal quotient of | #14657122, #14657127, #14657176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5757);