Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×C3⋊(ΓL(1,𝔽8)⋊Dic7) |
| unambiguous semidirect product | C3⋊(C19×ΓL(1,𝔽8)⋊Dic7) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C19×Dic21) |
| derived | C3×C72 ⋊ C3×C4×C19 |
| Hall | C3×C7×C19×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C4×C19 |
| Sylow | C72 ⋊ C3×Dic3×C19 |
136 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4788 |
2166 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 722);