Finite Group DatabasebetaFinite Group Databasebeta| order | 14272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C223 ⋊ #329 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7136 |
Polycyclic presentation:
2^6,223|a^2=d,c^2=f,d^2=e,b^a=bc,c^a=ce,g^a=g^222,c^b=cf,d^b=def1573 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43252940, #43252941, #43252943, … |
| maximal normal subgroup of | #43252940, #43252941, #43252943, … |
| maximal quotient of | #43252614, #43252619, #43252674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14272, 289);