Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C241 ⋊ C2 |
| Sylow | C241 ⋊ #578 |
248 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^240,e^b=ef,g^b=g^240,d^c=df2422 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44509407, #44509411, #44509421, … |
| maximal normal subgroup of | #44509407, #44509411, #44509421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1366);