Finite Group DatabasebetaFinite Group Databasebeta| order | 20576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C643 ⋊ C2 |
| Sylow | C643 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5144 |
Polycyclic presentation:
2^5,643|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^642,c^b=ce,f^b=f^6425150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20576, 74);