Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C11 ⋊ #1307 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=e,d^2=g,e^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^10,c^b=cg,d^b=df,h^b=h^10166 conjugacy classes — view the full character table.
| maximal subgroup of | #14641319, #14641320, #14641397, … |
| maximal normal subgroup of | #14641319, #14641320, #14641397, … |
| maximal quotient of | #14640347, #14640349, #14640365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2421);