Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#432 ⋊ C2 |
| Sylow | C11 ⋊ #2981 |
402 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 402 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|a^2=f,f^2=g,b^a=be,d^a=de,h^a=h^10,c^b=ceg,d^b=dg,h^b=h^10,d^c=dg,h^c=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14650357, #14650361, #14650371, … |
| maximal normal subgroup of | #14650357, #14650361, #14650371, … |
| maximal quotient of | #14752493, #14752528, #14752775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13588);