Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C541 ⋊ C4 |
| Sylow | C541 ⋊ #443 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^6,541|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^489,d^b=df,g^b=g^540,g^c=g^52,g^e=g^540973 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 1593);