Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (Dic61⋊C3)⋊C25 |
| unambiguous semidirect product | (Dic61⋊C25)⋊C3 |
| derived, Sylow | C61 ⋊ C3×C4×C25 |
| Hall | Dic61⋊C25 ⋊ C3 |
| Hall | (C61⋊C3)⋊C25 ⋊ C4 |
| Hall | C61⋊C25 ⋊ C3×C4 |
| Hall | Dic61⋊C3 ⋊ C25 |
| Hall | Dic61 ⋊ C3×C25 |
| Hall | C61⋊C3 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C5 | (D61⋊C3)⋊C5 |
| commutator, hypocenter | C61 | C3×C4×C25 |
| Fitting, socle, cosocle | C2×C5×C61 | C2×C3×C5 |
| prime radical | C2×C5×C61⋊C3 | C2×C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6100 |
Polycyclic presentation:
2,3,5,61,2,5|a^2=e,c^5=f,d^a=d^60,d^b=d^47,d^c=d^20320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 2);