Finite Group DatabasebetaFinite Group Databasebeta| order | 34688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C4×Q8×C271 ⋊ C2 |
| Sylow | C271 ⋊ #3461 |
1012 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17344 |
Polycyclic presentation:
2^7,271|b^2=f,c^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,h^a=h^270,c^b=cf5444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34688, 17943);