Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #1623 |
228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 228 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) = 704 |
Polycyclic presentation:
2^7,11|b^2=f,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,d^b=df,e^b=eg,d^c=dg,e^c=eg,h^c=h^10136 conjugacy classes — view the full character table.
| maximal subgroup of | #14641603, #14641605, #14674542, … |
| maximal normal subgroup of | #14641603, #14641605, #14674542, … |
| maximal quotient of | #14642511, #14642548, #14642555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 3586);