Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q16×C241 ⋊ C2 |
| Sylow | C241 ⋊ #473 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|a^2=f,b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,e^c=ef,g^c=g^2401696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44509413, #44509415, #44509420, … |
| maximal normal subgroup of | #44509413, #44509415, #44509420, … |
| maximal quotient of | #44506807, #44506812, #44506831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 821);