Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×#14558808 |
| Fitting, socle | C2×C72×C19 ⋊ C2×C9 |
| derived | C7×C19 ⋊ C22×C7×C9 |
| Hall | C7×#11924781 ⋊ C22 |
| Hall | C2×C72×D19 ⋊ C9 |
| Hall | C72×C19 ⋊ C22×C9 |
| Hall | C2×D19 ⋊ C7×C7⋊C9 |
| Sylow | C72 ⋊ C2×AGL(1,𝔽19) |
| Sylow | C19 ⋊ C22×C7×C7⋊C9 |
160 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 798 |
518 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 906);