Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C211 ⋊ #1365 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27008 |
Polycyclic presentation:
2^7,211|a^2=d,b^2=eg,c^2=fg,d^2=efg,f^2=g,b^a=bc,c^a=ce,h^a=h^210,c^b=cf,d^b=def,f^b=fg2339 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 2568);