Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D541⋊#100 |
| Sylow | C541 ⋊ C2×#100 |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
Polycyclic presentation:
2^6,541|a^2=e,e^2=f,b^a=bd,d^a=df,g^a=g^52,e^b=ef,g^c=g^540,g^e=g^5401372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 1532);