Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#20269083 |
| Fitting, socle, Hall | C52×C37 ⋊ C4×C9 |
| derived | C5×C37 ⋊ C4×C5×C9 |
| Hall | C52×#66526 ⋊ C4 |
| Hall | C5×#10625192 ⋊ C9 |
| Hall | #66526 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C37 ⋊ C5×C9×AGL(1,𝔽5) |
| Sylow | C52 ⋊ AGL(1,𝔽37) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #20269083 |
| commutator, hypocenter | C5×C37 | C4×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C52×C37 | C4×C9 |
| prime radical | C5×C5⋊(D37⋊C3) | C2×C3 |
| cosocle | C5⋊(D37⋊C3) | C2×C3×C5 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C5 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 740 |
250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 439);