Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C11×C22⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #2648 |
484 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,d^2=f,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^10232 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2648, C2×#13074598, #14920305, … |
| maximal normal subgroup of | D11×#2648, C2×#13074598, #14920305, … |
| maximal quotient of | #14680227, #14680331, #14680391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 10492);