Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C239 ⋊ C2 |
| Sylow | C239 ⋊ #578 |
248 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^238,e^b=ef,g^b=g^238,d^c=df2402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486510, #44486514, #44486524, … |
| maximal normal subgroup of | #44486510, #44486514, #44486524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1366);