Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×SD16×#3866 |
| unambiguous semidirect product | D37⋊(C4×SD16) |
| Fitting | C2×SD16×C37 ⋊ C4 |
| Sylow | C37 ⋊ C2×C4×SD16 |
552 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 592 |
182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 21258);