Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C52×C37 ⋊ C3×C4 |
| derived | C5×C37 ⋊ C32×C4×C5 |
| Hall | C3×C52×C37⋊C3 ⋊ C4 |
| Hall | C5×AGL(1,𝔽5)×C37 ⋊ C32 |
| Hall | C52×C37 ⋊ C32×C4 |
| Sylow | C37 ⋊ C32×C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ C3×C4×C37⋊C3 |
156 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2220 |
1125 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 499);