Finite Group DatabasebetaFinite Group Databasebeta| order | 14272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D223)⋊C16 |
| Fitting | C2×C16×C223 ⋊ C2 |
| Sylow | C223 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7136 |
Polycyclic presentation:
2^6,223|a^2=d,d^2=e,e^2=f,b^a=bc,g^b=g^2223592 conjugacy classes. The character table is too large to display.
| maximal quotient of | #43252716, #43252732, #43252747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14272, 328);