Finite Group DatabasebetaFinite Group Databasebeta| order | 18486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | D3×(C79⋊C3)⋊C13 |
| unambiguous semidirect product | C3⋊(C2×(C79⋊C3)⋊C13) |
| unambiguous semidirect product | (D3×C79⋊C3)⋊C13 |
| unambiguous semidirect product | (D3×C79⋊C13)⋊C3 |
| Fitting, socle, derived | C3×C79 ⋊ C2×C3×C13 |
| Hall | C3×(C79⋊C3)⋊C13 ⋊ C2 |
| Hall | D3×C79⋊C3 ⋊ C13 |
| Hall | C79⋊C13 ⋊ C3×D3 |
| Hall | C3×C79⋊C3 ⋊ C2×C13 |
| Sylow | C79 ⋊ C3×D3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C79 | C2×C3×C13 |
| LCS | G ▷ C3×C79 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 237 |
123 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽79), C2×D3×(C79⋊C3)⋊C13 |
| maximal normal subgroup of | D3×AGL(1,𝔽79), C2×D3×(C79⋊C3)⋊C13 |
| maximal quotient of | Dic3×(C79⋊C3)⋊C13, C2×D3×(C79⋊C3)⋊C13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18486, 34);