Finite Group DatabasebetaFinite Group Databasebeta| order | 36544 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C16×C571 ⋊ C2 |
| Sylow | C571 ⋊ #357 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18272 |
Polycyclic presentation:
2^6,571|a^2=d,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^570,c^b=ce,e^b=ef,g^b=g^5709142 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36544, 351);