Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M64×C211 ⋊ C2 |
| Sylow | C211 ⋊ #1401 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13504 |
Polycyclic presentation:
2^7,211|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^210,c^b=cg,d^b=dg,h^b=h^2104256 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 2653);