Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C241 ⋊ #476 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|a^2=df,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^240,e^c=ef2419 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44506561, #44506563, #44506572, … |
| maximal normal subgroup of | #44506561, #44506563, #44506572, … |
| maximal quotient of | #44507445, #44507706, #44508030, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 839);