Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D52×C37⋊C3 |
| unambiguous semidirect product | (C5×D5)⋊(C2×C3×C37⋊C3) |
| unambiguous semidirect product | (D52×C37)⋊C32 |
| unambiguous semidirect product | (C3×D52×C37)⋊C3 |
| Fitting, socle | C3×C52×C37 ⋊ C22×C3 |
| derived, Hall | C52×C37 ⋊ C22×C32 |
| Hall | C3×C52×C37⋊C3 ⋊ C22 |
| Hall | D52×C37 ⋊ C32 |
| Sylow | C37 ⋊ C32×D52 |
| Sylow | C52 ⋊ C22×C3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D52×C37⋊C3 |
| commutator, cosocle, hypocenter | C52×C37 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C37 | C22×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C3 | |
288 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1110 |
720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 506);