Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C137 ⋊ C2 |
| Sylow | C137 ⋊ #2398 |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8768 |
Polycyclic presentation:
2^7,137|a^2=e,b^2=e,d^2=ef,b^a=be,c^a=cf,h^a=h^136,c^b=cg2764 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 7797);