Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D541⋊(C4⋊C8) |
| Sylow | C541 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17312 |
Polycyclic presentation:
2^6,541|a^2=e,b^2=d,e^2=f,b^a=bd,g^a=g^52,g^c=g^540,g^e=g^5402200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 1550);