Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #2153 |
152 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 89 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=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,c^b=cg,h^b=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14669887, #14669888, #14669891, … |
| maximal normal subgroup of | #14669887, #14669888, #14669891, … |
| maximal quotient of | #14665320, #14665322, #14665346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6275);