Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D159⋊(D19⋊C3) |
| unambiguous semidirect product | (C3⋊(D19⋊C3))⋊D53 |
| unambiguous semidirect product | (C53⋊(D19⋊C3))⋊D3 |
| unambiguous semidirect product | (D57⋊D53)⋊C3 |
| Fitting, socle, derived | C3×C19×C53 ⋊ C22×C3 |
| Hall | C3×C53×C19⋊C3 ⋊ C22 |
| Hall | C19×C53 ⋊ C2×C3×D3 |
| Hall | C3×C19⋊C3 ⋊ C2×D53 |
| Sylow | C53 ⋊ D3×D19⋊C3 |
| Sylow | C19 ⋊ C3×D3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C53 | C22×C3 |
| LCS | G ▷ C3×C19×C53 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3021 |
Polycyclic presentation:
2^2,3^2,19,53|e^a=e^18,f^a=f^52,d^b=d^2,e^b=e^18,e^c=e^7495 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 80);