Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#436 ⋊ C2 |
| Sylow | C11 ⋊ #2967 |
362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,d^a=dg,h^a=h^10,c^b=cg,h^d=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2967, C2×#13077602, #15618287, … |
| maximal normal subgroup of | D11×#2967, C2×#13077602, #15618287, … |
| maximal quotient of | #14752013, #14752015, #14752027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13496);