Finite Group DatabasebetaFinite Group Databasebeta| order | 20382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C79 · Schur multiplier (H2) = C1 |
| direct product | C2×C79×C43⋊C3 |
| unambiguous semidirect product | (C2×C43)⋊(C3×C79) |
| Fitting, socle, Hall | C2×C43×C79 ⋊ C3 |
| derived, Sylow | C43 ⋊ C2×C3×C79 |
| Hall | C43×C79 ⋊ C2×C3 |
| Hall | C2×C43 ⋊ C3×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C79 | C43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C2×C3×C79 |
| Frattini | C1 | G |
| Fitting, socle | C2×C43×C79 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C79 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6794 |
2686 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20382, 3);