Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #518×C137 ⋊ C2 |
| Sylow | C137 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^7,137|a^2=g,e^2=g,b^a=bf,d^a=df,c^b=cf,h^e=h^1362380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 17714);