Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | 2−1+4×C239 ⋊ C2 |
| Sylow | C239 ⋊ #454 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3824 |
Polycyclic presentation:
2^6,239|c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^238,d^b=df,e^b=ef,d^c=df2039 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486564, #44486567, #44486572, … |
| maximal normal subgroup of | #44486564, #44486567, #44486572, … |
| maximal quotient of | #44483477, #44483483, #44483488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 722);