Finite Group DatabasebetaFinite Group Databasebeta| order | 2964 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D57 |
| unambiguous semidirect product | (C3×D13)⋊D19 |
| unambiguous semidirect product | (C19×D13)⋊D3 |
| Fitting, socle, derived, Hall | C3×C13×C19 ⋊ C22 |
| Hall | C13×C19 ⋊ C2×D3 |
| Hall | C3×C19 ⋊ C2×D13 |
| Hall | C3×C13 ⋊ C2×D19 |
| Sylow | C19 ⋊ D3×D13 |
| Sylow | C13 ⋊ C2×D57 |
| Sylow | C3 ⋊ D13×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C19 | C22 |
| LCS | G ▷ C3×C13×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 741 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D13×D57, D13×D285, D57×D65, … |
| maximal normal subgroup of | C5×D13×D57, C7×D13×D57, C11×D13×D57, … |
| maximal quotient of | C5×D13×D57, D13×D285, D57×D65, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2964, 58);