Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C19⋊C3)⋊#6157) |
| unambiguous semidirect product | (C19⋊C3)⋊(C3⋊#6157) |
| unambiguous semidirect product | (C3⋊(C19⋊#6157))⋊C3 |
| Fitting, socle, derived | C3×C19×C53 ⋊ C3×C4 |
| Hall | C3×C53×C19⋊C3 ⋊ C4 |
| Hall | C19×C53 ⋊ C3×Dic3 |
| Hall | C3×C19⋊C3 ⋊ #6157 |
| Sylow | C53 ⋊ C3⋊((C19⋊C3)⋊C4) |
| Sylow | C19 ⋊ C3×C3⋊#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C19×C53 | C3×C4 |
| prime radical | C3×C19⋊C3×D53 | C2 |
| cosocle | C3×C19×D53 | C2×C3 |
| LCS | G ▷ C3×C19×C53 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3021 |
Polycyclic presentation:
2,3,2,3,19,53|a^2=c,d^a=d^2,e^a=e^18,f^a=f^30,e^b=e^7,f^c=f^52387 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 75);