Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C11×C22⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #3538 |
1014 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=f,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,h^b=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | #14646062, #14646063, #14646066, … |
| maximal normal subgroup of | #14646062, #14646063, #14646066, … |
| maximal quotient of | #14916543, #14916752, #14916754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18755);