Finite Group DatabasebetaFinite Group Databasebeta| order | 36928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C42×C577 ⋊ C4 |
| Sylow | C577 ⋊ #354 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9232 |
Polycyclic presentation:
2^6,577|a^2=d,b^2=f,c^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^553,c^b=cf,d^b=def,g^b=g^576,d^c=df,g^d=g^5762317 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36928, 1456);