Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#487 ⋊ C2 |
| Sylow | C11 ⋊ #3364 |
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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|b^2=eg,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^10,d^b=de,h^b=h^10,f^c=fg,h^c=h^10145 conjugacy classes — view the full character table.
| maximal subgroup of | #14743704, #14743711, #14743809, … |
| maximal normal subgroup of | #14743704, #14743711, #14743809, … |
| maximal quotient of | #14770392, #14770574, #14772720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17200);