Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C541 ⋊ C2 |
| Sylow | C541 ⋊ #510 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17312 |
Polycyclic presentation:
2^6,541|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^540,d^b=de,e^b=ef,g^b=g^5405416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 992);