Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C11×C4⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #2361 |
788 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=eg,d^2=e,b^a=be,c^a=cf,h^a=h^10,d^b=de250 conjugacy classes — view the full character table.
| maximal subgroup of | #14774038, #14774045, #14774083, … |
| maximal normal subgroup of | #14774038, #14774045, #14774083, … |
| maximal quotient of | C4⋊C4×C22⋊Dic11, #14675266, #14675341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7526);