Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic305⋊C5) |
| unambiguous semidirect product | Dic915⋊C5 |
| derived | C3×C5×C61 ⋊ C4×C5 |
| Hall | C3×C5×C61⋊C5 ⋊ C4 |
| Hall | C5×C61⋊C5 ⋊ Dic3 |
| Hall | C3×C61 ⋊ C5×Dic5 |
| Sylow | C61 ⋊ C5×Dic15 |
| Sylow | C3 ⋊ Dic305⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C5⋊(D61⋊C5)) |
| commutator, hypocenter | C3×C5×C61 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C5×C61 | C2×C5 |
| prime radical | C2×C3×C5×C61⋊C5 | C2 |
| LCS | G ▷ C3×C5×C61 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3660 |
Polycyclic presentation:
2,5,3,5,61,2|a^2=f,c^a=c^2,d^a=d^4,e^a=e^60,e^b=e^9270 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 81);