Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#16861520⋊C3) |
| unambiguous semidirect product | (C3⋊#16861520)⋊C3 |
| Fitting, socle, derived | C3×C52×C41 ⋊ C3×C4 |
| Hall | C3×C41×C52⋊C3 ⋊ C4 |
| Hall | C52×C41 ⋊ C3×Dic3 |
| Hall | C3×C52⋊C3 ⋊ Dic41 |
| Sylow | C41 ⋊ C3⋊(#1043⋊C3) |
| Sylow | C52 ⋊ C3×Dic123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C41 | C3×C4 |
| prime radical | C3×C41×(C5⋊D5)⋊C3 | C2 |
| cosocle | C3×C41×C5⋊D5 | C2×C3 |
| LCS | G ▷ C3×C52×C41 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1845 |
Polycyclic presentation:
2,3,2,3,5^2,41|a^2=c,d^a=d^2,e^a=e^2,f^a=f^2,g^a=g^40,e^b=e^3f^4,f^b=e^3f,e^c=e^4,f^c=f^4624 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 427);