Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C37 ⋊ C2 |
| Sylow | C37 ⋊ #3055 |
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^7,37|b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^c=h^36428 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 14123);