Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| direct product | #4380×C41⋊C5 |
| unambiguous semidirect product | (C41×#4380)⋊C5 |
| Fitting, socle, derived | C32×C5×C41 ⋊ C4×C5 |
| Hall | C32×C5×C41⋊C5 ⋊ C4 |
| Hall | C5×C41⋊C5 ⋊ #157 |
| Hall | C32×C41 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C41 ⋊ C5×#4380 |
| Sylow | C32 ⋊ AGL(1,𝔽5)×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C41 | C4×C5 |
| prime radical | C3⋊D15×C41⋊C5 | C2 |
| cosocle | C41×C3⋊D15 | C2×C5 |
| LCS | G ▷ C32×C5×C41 | |
| UCS | C1 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1230 |
195 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 346);