Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic61⋊C25) |
| unambiguous semidirect product | Dic183⋊C25 |
| derived, Hall | C3×C61 ⋊ C4×C25 |
| Hall | C3×C61⋊C25 ⋊ C4 |
| Hall | C61⋊C25 ⋊ Dic3 |
| Hall | Dic183 ⋊ C25 |
| Sylow | C61 ⋊ Dic3×C25 |
| Sylow | C3 ⋊ Dic61⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C5 | C3⋊(D61⋊C5) |
| commutator, hypocenter | C3×C61 | C4×C25 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C61 | C2×C5 |
| LCS | G ▷ C3×C61 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18300 |
Polycyclic presentation:
2,5,3,61,2,5|a^2=e,b^5=f,c^a=c^2,d^a=d^60,d^b=d^9330 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 6);