Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #123×C137 ⋊ C4 |
| Sylow | C137 ⋊ #2322 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^7,137|a^2=g,b^2=g,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^37,c^b=ce,h^b=h^100,h^g=h^136520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 20996);