Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C211 ⋊ #1491 |
252 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 13504 |
Polycyclic presentation:
2^7,211|a^2=e,b^2=f,c^2=f,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^210,c^b=cf,d^b=df,h^b=h^2104238 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 2958);