Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C4×ΓL(1,𝔽8)×#87704 |
| Fitting, Hall | C4×C72×C19 ⋊ C32 |
| derived, Hall | C72×C19 ⋊ C32×C4 |
| Hall | C4×C72 ⋊ C3×C19⋊C3 |
| Hall | C4×C19 ⋊ ΓL(1,𝔽8)2 |
| Sylow | C72 ⋊ C3×C4×C19⋊C3 |
| Sylow | C19 ⋊ C4×ΓL(1,𝔽8)2 |
168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 168 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) = 1596 |
940 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 624);