Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#446 ⋊ C2 |
| Sylow | C11 ⋊ #2968 |
372 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,h^b=h^10,d^c=dg,h^c=h^10,h^d=h^10190 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2968, C2×#13077609, #15618312, … |
| maximal normal subgroup of | D11×#2968, C2×#13077609, #15618312, … |
| maximal quotient of | #14752040, #14752046, #14752067, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13503);