Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#30660585 |
| derived, Hall | C72×C19 ⋊ C22×C9 |
| Hall | #22552710 ⋊ C22 |
| Hall | C2×C7×D7×C19 ⋊ C9 |
| Hall | C2×C7×D7 ⋊ #4294 |
| Sylow | C72 ⋊ C22×#4294 |
| Sylow | C19 ⋊ C2×#11725076 |
156 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4788 |
1362 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 430);