Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C137 ⋊ C2 |
| Sylow | C137 ⋊ #2342 |
792 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^7,137|a^2=g,b^2=f,b^a=be,c^a=cf,h^a=h^136,d^b=de,h^b=h^136,h^d=h^1362770 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 7362);