Finite Group DatabasebetaFinite Group Databasebeta| order | 21294 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×D507 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)×D169) |
| Fitting, derived | C3×C7×C169 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8)×C169 ⋊ C2 |
| Hall | C7×C169 ⋊ C3×D3 |
| Sylow | C169 ⋊ D3×ΓL(1,𝔽8) |
| Hall | C3×ΓL(1,𝔽8) ⋊ D169 |
| Sylow | C7 ⋊ C3×D507 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C7×C169 | C2×C3 |
| Frattini | C13 | ΓL(1,𝔽8)×D39 |
| socle | C3×C7×C13 | C3×D13 |
| LCS | G ▷ C3×C7×C169 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3549 |
1275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21294, 47);