Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #1981 |
324 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 129 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=f,b^2=df,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^10,d^b=dg,f^b=fg,h^b=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | #14645703, #14645704, #14645717, … |
| maximal normal subgroup of | #14645703, #14645704, #14645717, … |
| maximal quotient of | #14652726, #14652744, #14652804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5434);