Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊(#10625193⋊C3) |
| unambiguous semidirect product | C3⋊(C5×#10625193⋊C3) |
| unambiguous semidirect product | (C3⋊#10625193)⋊(C3×C5) |
| unambiguous semidirect product | (C5×C3⋊#10625193)⋊C3 |
| Fitting, socle | C3×C52×C37 ⋊ C3×C4 |
| derived | C3×C5×C37 ⋊ C3×C4×C5 |
| Hall | C3×C52×C37⋊C3 ⋊ C4 |
| Hall | C52×C37 ⋊ C3×Dic3 |
| Hall | C3×C37⋊C3 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C37 ⋊ C3×C5×ΓL(1,𝔽16) |
| Sylow | C52 ⋊ C3⋊(Dic37⋊C3) |
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2220 |
495 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 566);