Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#466 ⋊ C2 |
| Sylow | C11 ⋊ #3062 |
504 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^b=h^10,d^c=dg,h^c=h^10,h^d=h^10142 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3062, C2×#13078295, #15621024, … |
| maximal normal subgroup of | D11×#3062, C2×#13078295, #15621024, … |
| maximal quotient of | #14737256, #14737278, #14737300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14189);