Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C11×#417 ⋊ C2 |
| Sylow | C11 ⋊ #3007 |
754 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^10,e^b=eg,h^c=h^10142 conjugacy classes — view the full character table.
| maximal subgroup of | #14791046, #14791050, #14791057, … |
| maximal normal subgroup of | #14791046, #14791050, #14791057, … |
| maximal quotient of | #14726177, #14726216, #14726255, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13771);