Finite Group DatabasebetaFinite Group Databasebeta| order | 14272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C223⋊C16) |
| Sylow | C223 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14272 |
Polycyclic presentation:
2^6,223|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^2223592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43252748, #43252749, #43252751, … |
| maximal normal subgroup of | #43252748, #43252749, #43252751, … |
| maximal quotient of | #43252857, #43252863, #43252871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14272, 368);