Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C11×C22⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #2620 |
612 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 157 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|a^2=ef,d^2=e,b^a=be,c^a=cf,h^a=h^10,c^b=cg,d^c=de,h^c=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | #14792008, #14792009, #14792036, … |
| maximal normal subgroup of | #14792008, #14792009, #14792036, … |
| maximal quotient of | #14680146, #14680152, #14680173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 10272);