Finite Group DatabasebetaFinite Group Databasebeta| order | 14272 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C223 ⋊ #343 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7136 |
Polycyclic presentation:
2^6,223|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=cf,g^a=g^222,d^b=df2242 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43252796, #43252797, #43252799, … |
| maximal normal subgroup of | #43252796, #43252797, #43252799, … |
| maximal quotient of | #43252636, #43252643, #43252649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14272, 318);