Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C211 ⋊ #1770 |
272 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 27008 |
Polycyclic presentation:
2^7,211|a^2=e,b^2=f,c^2=de,e^2=g,b^a=bd,h^a=h^210,c^b=cg,h^b=h^210,h^c=h^2104256 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 4380);