Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16861520⋊C9 |
| derived, Hall | C52×C41 ⋊ C4×C9 |
| Hall | C41×C52⋊C9 ⋊ C4 |
| Hall | #16861520 ⋊ C9 |
| Hall | C52⋊C9 ⋊ Dic41 |
| Sylow | C41 ⋊ #1043⋊C9 |
| Sylow | C52 ⋊ C9×Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #16861520⋊C3 |
| commutator, hypocenter | C52×C41 | C4×C9 |
| Fitting, socle | C3×C52×C41 | C3×C4 |
| prime radical, cosocle | C3×C41×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52×C41 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1845 |
Polycyclic presentation:
2,3,2,5^2,41,3|a^2=c,b^3=g,d^a=d^3,e^a=e^3,f^a=f^40,d^b=d^3e^3,e^b=d^4e,d^c=d^4,e^c=e^4642 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 204);