Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q32×C239 ⋊ C2 |
| Sylow | C239 ⋊ SD64 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,c^b=cd,d^b=de,e^b=ef,g^b=g^2381328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD64×D239, C2×#29504609, #44486855, … |
| maximal normal subgroup of | SD64×D239, C2×#29504609, #44486855, … |
| maximal quotient of | #44482725, #44482729, #44482749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 386);