Finite Group DatabasebetaFinite Group Databasebeta| order | 23780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic1189⋊C5 |
| derived, Hall | C29×C41 ⋊ C4×C5 |
| Hall | C29×C41⋊C5 ⋊ C4 |
| Hall | Dic1189 ⋊ C5 |
| Hall | C41⋊C5 ⋊ Dic29 |
| Sylow | C41 ⋊ C5×Dic29 |
| Sylow | C29 ⋊ Dic41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C29⋊(D41⋊C5) |
| commutator, hypocenter | C29×C41 | C4×C5 |
| Fitting, socle, cosocle | C2×C29×C41 | C2×C5 |
| prime radical | C2×C29×C41⋊C5 | C2 |
| LCS | G ▷ C29×C41 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4756 |
Polycyclic presentation:
2,5,29,41,2|a^2=e,c^a=c^28,d^a=d^40,d^b=d^10392 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23780, 12);