Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #99×C239 ⋊ C2 |
| Sylow | C239 ⋊ #353 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1912 |
Polycyclic presentation:
2^6,239|a^2=d,c^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cf,d^b=def,g^b=g^238,d^c=df1322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #353×D239, C2×#29504564, #44486211, … |
| maximal normal subgroup of | #353×D239, C2×#29504564, #44486211, … |
| maximal quotient of | #44482479, #44482493, #44482544, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 341);