Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×#66526⋊C2 |
| unambiguous semidirect product | (C5×#66526⋊C2)⋊(C2×C5) |
| unambiguous semidirect product | (C5⋊(#66526⋊C2))⋊(C2×C5) |
| unambiguous semidirect product | (D5×#66526)⋊(C2×C5) |
| Fitting, socle, Hall | C52×C37 ⋊ C22×C9 |
| derived | C5×C37 ⋊ C22×C5×C9 |
| Hall | C52×#66526 ⋊ C22 |
| Hall | C5×D5×D37 ⋊ C9 |
| Hall | #66526 ⋊ C2×C5×D5 |
| Sylow | C37 ⋊ C2×C5×C9×D5 |
| Sylow | C52 ⋊ C2×#66526⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×#66526⋊C2 |
| commutator, hypocenter | C5×C37 | C22×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C52×C37 | C22×C9 |
| prime radical | C5×D5×D37⋊C3 | C3 |
| cosocle | C5×C37⋊C3 | C22×C3×C5 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C5 | |
144 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 370 |
400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 437);