Finite Group DatabasebetaFinite Group Databasebeta| order | 19740 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic235 |
| unambiguous semidirect product | C47⋊(Dic5×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×Dic235)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)×D235 |
| commutator, hypocenter | C5×C7×C47 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C7×C47 | C2×C3 |
| prime radical | C2×C5×ΓL(1,𝔽8)×C47 | C2 |
| LCS | G ▷ C5×C7×C47 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6580 |
1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19740, 22);