Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #338×C211 ⋊ C2 |
| Sylow | C211 ⋊ #2069 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3376 |
Polycyclic presentation:
2^7,211|a^2=de,b^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^210,c^b=cf,f^b=fg,h^b=h^210,d^c=dg,h^c=h^2102333 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 5909);