Finite Group DatabasebetaFinite Group Databasebeta| order | 3822 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D7×#63270 |
| Fitting, socle, derived, Hall | C72×C13 ⋊ C2×C3 |
| Hall | C7×#63270 ⋊ C2 |
| Hall | C7×C13×D7 ⋊ C3 |
| Hall | C7×D7 ⋊ C13⋊C3 |
| Sylow | C72 ⋊ C2×C13⋊C3 |
| Sylow | C13 ⋊ D7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C13 | C2×C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 546 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#63270, #26039539, #26039542, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#63270, #26039539, #26039542, … |
| maximal quotient of | D7×#11717941, C3×D7×#63270, D21×#63270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3822, 74);