Finite Group DatabasebetaFinite Group Databasebeta| order | 4716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D393 |
| unambiguous semidirect product | (C3×D3)⋊D131 |
| unambiguous semidirect product | (D3×C131)⋊D3 |
| Fitting, socle, derived, Hall | C32×C131 ⋊ C22 |
| Sylow | C131 ⋊ D32 |
| Sylow | C32 ⋊ C2×D131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C131 | C22 |
| LCS | G ▷ C32×C131 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 786 |
594 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C3⋊(D131⋊C5), C5×D3×D393, D3×D1965, … |
| maximal normal subgroup of | D3×C3⋊(D131⋊C5), C5×D3×D393, D3×C7×D393 |
| maximal quotient of | C5×D3×D393, D3×D1965, D15×D393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4716, 21);