Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#448 ⋊ C2 |
| Sylow | C11 ⋊ #3196 |
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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|b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^10,f^c=fg121 conjugacy classes — view the full character table.
| maximal subgroup of | #14727933, #14727935, #14728001, … |
| maximal normal subgroup of | #14727933, #14727935, #14728001, … |
| maximal quotient of | #14762851, #14762860, #14764061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15337);