Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#16864520 |
| Sylow | C541 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34624 |
Polycyclic presentation:
2^6,541|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^52,c^b=ce,g^d=g^5401378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 1398);