Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#478 ⋊ C2 |
| Sylow | C11 ⋊ #3114 |
450 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^10,h^b=h^10,d^c=dg,f^c=fg,h^d=h^10127 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3114, C2×#13078759, #15621989, … |
| maximal normal subgroup of | D11×#3114, C2×#13078759, #15621989, … |
| maximal quotient of | #14753823, #14756794, #14756796, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14653);