Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #100×C241 ⋊ C2 |
| Sylow | C241 ⋊ #453 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1928 |
Polycyclic presentation:
2^6,241|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^240,d^b=df,e^b=ef,g^b=g^240,d^c=df1336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44509430, #44509442, #44509453, … |
| maximal normal subgroup of | #44509430, #44509442, #44509453, … |
| maximal quotient of | #44506365, #44506370, #44506393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 719);