Finite Group DatabasebetaFinite Group Databasebeta| order | 3822 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C7×C13×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C3×C7×C13) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C2×C7×C13) |
| Fitting, socle, Hall | C72×C13 ⋊ C2×C3 |
| derived | C7 ⋊ C2×C3×C7×C13 |
| Hall | C7×C13×ΓL(1,𝔽8) ⋊ C2 |
| Hall | C7×C13×D7 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×C13 |
| Hall | C7×D7 ⋊ C3×C13 |
| Sylow | C72 ⋊ C2×C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C13 | AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C7 | C2×C3×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C72×C13 | C2×C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C7×C13 | |
34 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 546 |
637 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3822, 27);