Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D5×C5⋊(#66526⋊C2) |
| unambiguous semidirect product | (C5×D5)⋊(#66526⋊C2) |
| unambiguous semidirect product | (D5×#66526)⋊D5 |
| Fitting, socle, derived, Hall | C52×C37 ⋊ C22×C9 |
| Hall | C52×#66526 ⋊ C22 |
| Hall | D5×D185 ⋊ C9 |
| Hall | #66526 ⋊ D52 |
| Sylow | C37 ⋊ C9×D52 |
| Sylow | C52 ⋊ C2×#66526⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C37 | C22×C9 |
| prime radical | D5×C5⋊(D37⋊C3) | C3 |
| cosocle | C52×C37⋊C3 | C22×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
144 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 370 |
184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 446);