Finite Group DatabasebetaFinite Group Databasebeta| order | 36150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D241⋊C25) |
| unambiguous semidirect product | D723⋊C25 |
| unambiguous semidirect product | (C241⋊C25)⋊D3 |
| derived, Hall | C3×C241 ⋊ C2×C25 |
| Hall | C3×C241⋊C25 ⋊ C2 |
| Hall | C241⋊C25 ⋊ D3 |
| Hall | D723 ⋊ C25 |
| Sylow | C241 ⋊ D3×C25 |
| Sylow | C3 ⋊ D241⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C3⋊(D241⋊C5) |
| commutator, hypocenter | C3×C241 | C2×C25 |
| Fitting, socle, cosocle | C3×C5×C241 | C2×C5 |
| prime radical | C5×D723 | C5 |
| LCS | G ▷ C3×C241 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18075 |
Polycyclic presentation:
2,3,5,241,5|c^5=e,b^a=b^2,d^a=d^240,d^c=d^91435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36150, 14);