Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D8×C239 ⋊ C2 |
| Sylow | C239 ⋊ #466 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,g^c=g^2381688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486458, #44486463, #44486468, … |
| maximal normal subgroup of | #44486458, #44486463, #44486468, … |
| maximal quotient of | #44483900, #44483905, #44483934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 782);