Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #1629 |
314 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 65 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=f,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^10,d^b=df,e^b=eg,d^c=dg,e^c=eg151 conjugacy classes — view the full character table.
| maximal subgroup of | #14674487, D11×#1629, C2×#13067732, … |
| maximal normal subgroup of | #14674487, D11×#1629, C2×#13067732, … |
| maximal quotient of | #14642560, #14642584, #14642741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 3626);