Finite Group DatabasebetaFinite Group Databasebeta| order | 14516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic191⋊C19 |
| unambiguous semidirect product | (C191⋊C19)⋊C4 |
| derived, Sylow | C191 ⋊ C4×C19 |
| Hall | C191⋊C19 ⋊ C4 |
| Hall | Dic191 ⋊ C19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D191⋊C19 |
| commutator, hypocenter | C191 | C4×C19 |
| Fitting, socle, cosocle | C2×C191 | C2×C19 |
| prime radical | C2×C191⋊C19 | C2 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 764 |
Polycyclic presentation:
2,19,191,2|a^2=d,c^a=c^190,c^b=c^5286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14516, 2);