Finite Group DatabasebetaFinite Group Databasebeta| order | 14272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊(C223⋊C8) |
| Sylow | C223 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14272 |
Polycyclic presentation:
2^6,223|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^222,c^b=ce2248 conjugacy classes. The character table is too large to display.
| maximal quotient of | #43252616, #43252619, #43252634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14272, 280);