Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#26013840 |
| derived, Hall | C72×C19 ⋊ C32×C4 |
| Hall | C3×C7×#87705 ⋊ C4 |
| Hall | C7⋊Dic133 ⋊ C32 |
| Sylow | C72 ⋊ C3×(C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ C3×ΓL(1,𝔽8)⋊Dic7 |
168 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 168 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 |
1014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 664);