Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C11×Q16 ⋊ C2 |
| Sylow | C11 ⋊ #3059 |
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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=g,b^2=eg,e^2=g,b^a=be,c^a=cf,e^a=eg,d^c=dg,h^c=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | #14671224, #14671239, #14672510, … |
| maximal normal subgroup of | #14671224, #14671239, #14672510, … |
| maximal quotient of | #14736847, #14736886, #14736936, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14161);