Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #328×C211 ⋊ C2 |
| Sylow | C211 ⋊ #1603 |
244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6752 |
Polycyclic presentation:
2^7,211|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^210,d^b=df,e^b=eg,h^b=h^210,d^c=dg,h^c=h^2102018 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 3476);