Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C241 ⋊ #490 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,c^b=cf,g^b=g^240,g^c=g^2401696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44505615, #44506736, #44506741, … |
| maximal normal subgroup of | #44505615, #44506736, #44506741, … |
| maximal quotient of | #44507580, #44508145, #44508270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 913);