Finite Group DatabasebetaFinite Group Databasebeta| order | 19530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×D31⋊C5 |
| unambiguous semidirect product | (D31×C7⋊C9)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×D31⋊C5 |
| commutator, hypocenter | C7×C31 | C2×C5×C9 |
| Fitting, socle, cosocle | C3×C7×C31 | C2×C3×C5 |
| prime radical | C3×C7×D31⋊C5 | C3 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1953 |
195 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19530, 62);