Finite Group DatabasebetaFinite Group Databasebeta| order | 3612 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D21×D43 |
| unambiguous semidirect product | (C3×D43)⋊D7 |
| unambiguous semidirect product | (C7×D43)⋊D3 |
| Fitting, socle, derived, Hall | C3×C7×C43 ⋊ C22 |
| Hall | C7×C43 ⋊ C2×D3 |
| Hall | C3×C43 ⋊ C2×D7 |
| Sylow | C43 ⋊ C2×D21 |
| Hall | C3×C7 ⋊ C2×D43 |
| Sylow | C7 ⋊ D3×D43 |
| Sylow | C3 ⋊ D7×D43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C43 | C22 |
| LCS | G ▷ C3×C7×C43 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 903 |
276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D63, #14268588⋊D3, #14268587⋊D3, … |
| maximal normal subgroup of | #14268588⋊D3, #14268587⋊D3, D43×C3⋊AGL(1,𝔽7), … |
| maximal quotient of | D43×D63, C3×D21×D43, D43×C3⋊D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3612, 59);