Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C11×C4⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #3509 |
992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14645731, #14645735, #14646017, … |
| maximal normal subgroup of | #14645731, #14645735, #14646017, … |
| maximal quotient of | #14913917, #14914170, #14914222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18394);