Finite Group DatabasebetaFinite Group Databasebeta| order | 18426 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×D111 |
| unambiguous semidirect product | C3⋊(D37×C83) |
| unambiguous semidirect product | C37⋊(D3×C83) |
| Fitting, socle, Hall | C3×C37×C83 ⋊ C2 |
| derived, Hall | C3×C37 ⋊ C2×C83 |
| Hall | C37×C83 ⋊ D3 |
| Hall | C3×C83 ⋊ D37 |
| Sylow | C37 ⋊ D3×C83 |
| Sylow | C3 ⋊ D37×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C83 | D111 |
| commutator, cosocle, hypocenter | C3×C37 | C2×C83 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C83 | C2 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C83 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9213 |
4731 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D83×D111, D3×D37×C83, D111⋊D83, … |
| maximal normal subgroup of | D83×D111, D3×D37×C83, D111⋊D83, … |
| maximal quotient of | C83×Dic111, C2×C83×D111 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18426, 8);