Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#14515349 |
| Sylow | C241 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15424 |
Polycyclic presentation:
2^6,241|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^240,c^b=ce2428 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D241, C2×Q8⋊#14515349, #44505826, … |
| maximal normal subgroup of | Q8⋊C8×D241, C2×Q8⋊#14515349, #44505826, … |
| maximal quotient of | #44505268, #44505271, #44505286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 280);