Finite Group DatabasebetaFinite Group Databasebeta| order | 3668 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D131 |
| unambiguous semidirect product | (D7×C131)⋊C2 |
| unambiguous semidirect product | (C7×D131)⋊C2 |
| unambiguous semidirect product | D917⋊C2 |
| Fitting, socle, derived, Hall | C7×C131 ⋊ C22 |
| Sylow | C131 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C131 | C22 |
| LCS | G ▷ C7×C131 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 138 |
| transitive degree | μt(G) = 917 |
335 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽7)×D131, C3×D7×D131, D21×D131, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D131, C3×D7×D131, D7×D131⋊C5, … |
| maximal quotient of | C3×D7×D131, D21×D131, D7×D393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3668, 6);