Finite Group DatabasebetaFinite Group Databasebeta| order | 19530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | D7⋊C9×ΓL(1,𝔽32) |
| unambiguous semidirect product | D7⋊(C9×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C7⋊C9)⋊(C2×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×D7⋊C9)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | AGL(1,𝔽7)×ΓL(1,𝔽32) |
| commutator, hypocenter | C7×C31 | C2×C5×C9 |
| Fitting, socle, cosocle | C3×C7×C31 | C2×C3×C5 |
| prime radical | C3×D7×ΓL(1,𝔽32) | C3 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1953 |
231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19530, 66);