Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C11 ⋊ #1710 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=dg,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^b=h^10,h^c=h^10148 conjugacy classes — view the full character table.
| maximal subgroup of | #14668082, #14668083, #14668086, … |
| maximal normal subgroup of | #14668082, #14668083, #14668086, … |
| maximal quotient of | #14647549, #14653517, #14653521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4119);