Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C239 ⋊ C2 |
| Sylow | C239 ⋊ #472 |
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3824 |
Polycyclic presentation:
2^6,239|b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^b=g^238,e^c=ef1325 conjugacy classes. The character table is too large to display.
| maximal quotient of | #44483901, #44483906, #44483945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 817);