Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#405 ⋊ C2 |
| Sylow | C11 ⋊ #2955 |
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 185 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,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^10,e^b=eg,h^b=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14670642, #14670644, #14670688, … |
| maximal normal subgroup of | #14670642, #14670644, #14670688, … |
| maximal quotient of | C8×#66961, C8×#66962, #14723360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13414);