Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C32×C211 ⋊ C2 |
| Sylow | C211 ⋊ #1417 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13504 |
Polycyclic presentation:
2^7,211|a^2=d,c^2=ef,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^210,c^b=ce,e^b=ef,f^b=fg,h^b=h^2106758 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 2695);