Finite Group DatabasebetaFinite Group Databasebeta| order | 4179 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C199⋊C3 |
| unambiguous semidirect product | C199⋊(C3×C7) |
| Fitting, socle, Hall | C7×C199 ⋊ C3 |
| derived, Sylow | C199 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C199⋊C3 |
| commutator, cosocle, hypocenter | C199 | C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C199 | C3 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 206 |
| transitive degree | μt(G) = 1393 |
483 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#13184226, #27159961, #27159962, … |
| maximal normal subgroup of | C7×#13184226, #27159961, #27159962, … |
| maximal quotient of | C7×#13184224, C3×C7×C199⋊C3, C7×C22⋊(C199⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4179, 2);