Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C239 ⋊ C2 |
| Sylow | C239 ⋊ #508 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^238,d^b=de,e^b=ef,g^b=g^238,g^c=g^2381331 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486856, #44486858, #44486862, … |
| maximal normal subgroup of | #44486856, #44486858, #44486862, … |
| maximal quotient of | #44486254, #44486329, #44486394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 982);