Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #2095 |
254 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 93 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=d,b^2=de,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,h^a=h^10,c^b=cf,d^b=dg,e^b=eg,d^c=dg,e^c=eg172 conjugacy classes — view the full character table.
| maximal subgroup of | #14641381, #14641383, #14643036, … |
| maximal normal subgroup of | #14641381, #14641383, #14643036, … |
| maximal quotient of | #14658761, #14658796, #14658827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6048);