Finite Group DatabasebetaFinite Group Databasebeta| order | 36416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C569 ⋊ #504 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18208 |
Polycyclic presentation:
2^6,569|a^2=d,d^2=e,e^2=f,g^a=g^277,c^b=cf,g^b=g^568,g^c=g^568,g^d=g^483,g^e=g^568395 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36416, 1671);