Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C11×C22⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #2626 |
668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 668 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) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=f,b^a=be,c^a=cf,c^b=cg,h^b=h^10,d^c=de172 conjugacy classes — view the full character table.
| maximal subgroup of | #14649813, #14649823, #14654022, … |
| maximal normal subgroup of | #14649813, #14649823, #14654022, … |
| maximal quotient of | #14680185, #14680207, #14680315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 10317);