Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×#334 ⋊ C2 |
| Sylow | C11 ⋊ #1333 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=ceg,d^b=dg,e^b=eg,h^b=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1333, C2×#13066582, #14663537, … |
| maximal normal subgroup of | D11×#1333, C2×#13066582, #14663537, … |
| maximal quotient of | #14640427, #14640439, #14640539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2476);