Finite Group DatabasebetaFinite Group Databasebeta| order | 14272 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C223 ⋊ #341 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7136 |
Polycyclic presentation:
2^6,223|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^2223580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43252808, #43252809, #43252811, … |
| maximal normal subgroup of | #43252808, #43252809, #43252811, … |
| maximal quotient of | #43252628, #43252630, #43252655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14272, 314);