Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×SD16×C239 ⋊ C2 |
| Sylow | C239 ⋊ #460 |
128 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^238,e^c=ef1685 conjugacy classes. The character table is too large to display.
| maximal quotient of | #44483894, #44483898, #44483906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 747);