Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #1614 |
236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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=fg,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^10,d^b=df,e^b=eg,h^b=h^10,d^c=dg133 conjugacy classes — view the full character table.
| maximal subgroup of | #14666560, #14666561, #14666571, … |
| maximal normal subgroup of | #14666560, #14666561, #14666571, … |
| maximal quotient of | #14642819, #14642873, #14642906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 3537);