Finite Group DatabasebetaFinite Group Databasebeta| order | 20874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×ΓL(1,𝔽8)⋊D7 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(D7×C71) |
| Fitting, socle, Hall | C72×C71 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C3×C71 |
| Hall | C7×ΓL(1,𝔽8)×C71 ⋊ C2 |
| Hall | C71×C7⋊D7 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×C71 |
| Hall | C7⋊D7 ⋊ C3×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | ΓL(1,𝔽8)⋊D7 |
| commutator, cosocle, hypocenter | C72 | C2×C3×C71 |
| Frattini | C1 | G |
| Fitting, socle | C72×C71 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C71 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1491 |
1562 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20874, 35);