Finite Group DatabasebetaFinite Group Databasebeta| order | 20874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C71 · Schur multiplier (H2) = C7 |
| direct product | C71×C3⋊(C7⋊D7) |
| unambiguous semidirect product | C3⋊(C71×C7⋊D7) |
| unambiguous semidirect product | C7⋊(D21×C71) |
| Fitting, socle, Hall | C3×C72×C71 ⋊ C2 |
| derived, Hall | C3×C72 ⋊ C2×C71 |
| Hall | C72×C71 ⋊ D3 |
| Hall | C3×C71 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D3×C71 |
| Sylow | C3 ⋊ C71×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | C3⋊(C7⋊D7) |
| commutator, cosocle, hypocenter | C3×C72 | C2×C71 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C71 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C71 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10437 |
5325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20874, 61);