Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×#564 ⋊ C2 |
| Sylow | C11 ⋊ #1658 |
182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=g,c^2=f,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,h^a=h^10,d^b=df,e^b=eg,d^c=dg,e^c=efg115 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1658, C2×#13067918, #14734971, … |
| maximal normal subgroup of | D11×#1658, C2×#13067918, #14734971, … |
| maximal quotient of | #14642500, #14642527, #14643060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 3812);