Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C241 ⋊ C2 |
| Sylow | C241 ⋊ #480 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|c^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 | #44506429, #44506430, #44506440, … |
| maximal normal subgroup of | #44506429, #44506430, #44506440, … |
| maximal quotient of | #44507531, #44507633, #44507762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 862);