Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C11×C22⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #2395 |
560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^10,h^c=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14648751, #14648756, #14725932, … |
| maximal normal subgroup of | #14648751, #14648756, #14725932, … |
| maximal quotient of | #14675456, #14675472, #14675488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7770);