Finite Group DatabasebetaFinite Group Databasebeta| order | 23540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊Dic107 |
| unambiguous semidirect product | C107⋊(Dic11⋊C5) |
| unambiguous semidirect product | Dic1177⋊C5 |
| derived, Hall | C11×C107 ⋊ C4×C5 |
| Hall | C11⋊C5×C107 ⋊ C4 |
| Hall | Dic1177 ⋊ C5 |
| Sylow | C107 ⋊ Dic11⋊C5 |
| Hall | C11⋊C5 ⋊ Dic107 |
| Sylow | C11 ⋊ C5×Dic107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C11⋊C5)⋊D107 |
| commutator, hypocenter | C11×C107 | C4×C5 |
| Fitting, socle, cosocle | C2×C11×C107 | C2×C5 |
| prime radical | C2×C11⋊C5×C107 | C2 |
| LCS | G ▷ C11×C107 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4708 |
Polycyclic presentation:
2,5,11,107,2|a^2=e,c^a=c^10,d^a=d^106,c^b=c^4764 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23540, 12);