Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C241 ⋊ #382 |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15424 |
Polycyclic presentation:
2^6,241|a^2=f,b^2=e,c^2=d,b^a=bd,c^a=ce,g^b=g^240,g^c=g^2402428 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44505388, #44507453, #44507454, … |
| maximal normal subgroup of | #44505388, #44507453, #44507454, … |
| maximal quotient of | #44505671, #44505674, #44505701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 414);