Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#30660606 |
| derived, Hall | C72×C19 ⋊ C22×C9 |
| Hall | C7×#11924777 ⋊ C22 |
| Hall | C2×C7×D133 ⋊ C9 |
| Sylow | C72 ⋊ C2×#4294⋊C2 |
| Sylow | C19 ⋊ C2×D7×C7⋊C9 |
128 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4788 |
1032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 450);