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 ⋊ #2994 |
364 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,h^a=h^10,c^b=ceg,d^b=dg,h^b=h^10,h^c=h^10,h^d=h^10190 conjugacy classes — view the full character table.
| maximal subgroup of | #14724930, #14724934, #14724967, … |
| maximal normal subgroup of | #14724930, #14724934, #14724967, … |
| maximal quotient of | #14752572, #14752629, #14752680, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13673);