Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×ΓL(1,𝔽8)×Dic21 |
| unambiguous semidirect product | C3⋊(C19×ΓL(1,𝔽8)×Dic7) |
| 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 |
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4788 |
2280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 738);