Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C211 ⋊ #1838 |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13504 |
Polycyclic presentation:
2^7,211|a^2=f,b^2=e,c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cg,h^b=h^210,h^c=h^2102972 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 4650);