Finite Group DatabasebetaFinite Group Databasebeta| order | 14272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C223 ⋊ C2 |
| Sylow | C223 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7136 |
Polycyclic presentation:
2^6,223|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^222,c^b=ce,g^b=g^2223580 conjugacy classes. The character table is too large to display.
| maximal quotient of | #43252613, #43252615, #43252633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14272, 278);