Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #124×C241 ⋊ C2 |
| Sylow | C241 ⋊ #454 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3856 |
Polycyclic presentation:
2^6,241|c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,g^b=g^240,d^c=df1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44505595, #44505597, #44509462, … |
| maximal normal subgroup of | #44505595, #44505597, #44509462, … |
| maximal quotient of | #44506372, #44506379, #44506384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 721);