Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×SD16×C239 ⋊ C2 |
| Sylow | C239 ⋊ #448 |
158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 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=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,g^c=g^2381685 conjugacy classes. The character table is too large to display.
| maximal quotient of | #44483469, #44483486, #44483537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 686);