Finite Group DatabasebetaFinite Group Databasebeta| order | 20874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| Fitting, socle | C2×C7×C71 ⋊ C3×C7 |
| derived | C7×C71 ⋊ C2×C3×C7 |
| Hall | C2×C7×C71⋊C7 ⋊ C3 |
| Hall | C7×C71⋊C7 ⋊ C2×C3 |
| Hall | C2×C71 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C71 ⋊ C2×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)×C71⋊C7 |
| commutator, cosocle, hypocenter | C7×C71 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C71 | C3×C7 |
| LCS | G ▷ C7×C71 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 994 |
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20874, 21);