Finite Group DatabasebetaFinite Group Databasebeta| order | 36224 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | C283⋊#1309 |
| Sylow | C283 ⋊ #1309 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18112 |
Polycyclic presentation:
2^7,283|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,c^a=cf,e^a=eg,c^b=cg,d^b=df,h^b=h^2823974 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36224, 2423);