Finite Group DatabasebetaFinite Group Databasebeta| order | 18860 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(Dic41⋊C5) |
| unambiguous semidirect product | Dic943⋊C5 |
| derived, Hall | C23×C41 ⋊ C4×C5 |
| Hall | C23×C41⋊C5 ⋊ C4 |
| Hall | Dic943 ⋊ C5 |
| Hall | C41⋊C5 ⋊ Dic23 |
| Sylow | C41 ⋊ C5×Dic23 |
| Sylow | C23 ⋊ Dic41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C23⋊(D41⋊C5) |
| commutator, hypocenter | C23×C41 | C4×C5 |
| Fitting, socle, cosocle | C2×C23×C41 | C2×C5 |
| prime radical | C2×C23×C41⋊C5 | C2 |
| LCS | G ▷ C23×C41 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3772 |
Polycyclic presentation:
2,5,23,41,2|a^2=e,c^a=c^22,d^a=d^40,d^b=d^10314 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18860, 12);