Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #1336 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|a^2=d,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^10,c^b=ceg,d^b=dg,e^b=eg172 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1336, C2×#13066592, #14663566, … |
| maximal normal subgroup of | D11×#1336, C2×#13066592, #14663566, … |
| maximal quotient of | #14640428, #14640431, #14640434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2486);