Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C239⋊C16) |
| Sylow | C239 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15296 |
Polycyclic presentation:
2^6,239|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^2383848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44482503, #44482504, #44482506, … |
| maximal normal subgroup of | #44482503, #44482504, #44482506, … |
| maximal quotient of | #44482612, #44482618, #44482626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 368);