Finite Group DatabasebetaFinite Group Databasebeta| order | 18906 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C137 · Schur multiplier (H2) = C1 |
| direct product | C137×D69 |
| unambiguous semidirect product | C3⋊(D23×C137) |
| unambiguous semidirect product | C23⋊(D3×C137) |
| Fitting, socle, Hall | C3×C23×C137 ⋊ C2 |
| derived, Hall | C3×C23 ⋊ C2×C137 |
| Hall | C23×C137 ⋊ D3 |
| Hall | C3×C137 ⋊ D23 |
| Sylow | C23 ⋊ D3×C137 |
| Sylow | C3 ⋊ D23×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C137 | D69 |
| commutator, cosocle, hypocenter | C3×C23 | C2×C137 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C137 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C137 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9453 |
4932 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D69×D137, D3×D23×C137, D69⋊D137, … |
| maximal normal subgroup of | D69×D137, D3×D23×C137, D69⋊D137, … |
| maximal quotient of | C137×Dic69, C2×C137×D69 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18906, 7);