Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#577 ⋊ C2 |
| Sylow | C11 ⋊ #3288 |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=de,e^b=eg,f^c=fg,h^c=h^10,e^d=eg136 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3288, C2×#13080378, #15629970, … |
| maximal normal subgroup of | D11×#3288, C2×#13080378, #15629970, … |
| maximal quotient of | #14743114, #14743121, #14743135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16272);