Finite Group DatabasebetaFinite Group Databasebeta| order | 4662 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×D111 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)×D37) |
| Fitting, socle, derived | C3×C7×C37 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8)×C37 ⋊ C2 |
| Hall | C7×C37 ⋊ C3×D3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ D37 |
| Sylow | C37 ⋊ D3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×D111 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C37 | C2×C3 |
| LCS | G ▷ C3×C7×C37 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 777 |
285 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×ΓL(1,𝔽8)×D111, ΓL(1,𝔽8)×D555, C49⋊C3×D111, … |
| maximal normal subgroup of | C5×ΓL(1,𝔽8)×D111, C7×ΓL(1,𝔽8)×D111 |
| maximal quotient of | C5×ΓL(1,𝔽8)×D111, ΓL(1,𝔽8)×D555, C49⋊C3×D111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4662, 67);