Finite Group DatabasebetaFinite Group Databasebeta| order | 34688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C271 ⋊ #2178 |
146 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^7,271|a^2=e,c^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^270,d^b=df,f^b=fg,h^c=h^2703014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34688, 6391);