Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #356×C211 ⋊ C2 |
| Sylow | C211 ⋊ #1410 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3376 |
Polycyclic presentation:
2^7,211|a^2=d,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cfg,d^b=def,e^b=eg,h^b=h^210,d^c=dfg,e^d=eg1382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 2676);