Finite Group DatabasebetaFinite Group Databasebeta| order | 18798 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C241 · Schur multiplier (H2) = C1 |
| direct product | D3×C13×C241 |
| unambiguous semidirect product | C3⋊(C2×C13×C241) |
| Fitting, socle, Hall | C3×C13×C241 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C13×C241 |
| Hall | C3×C241 ⋊ C2×C13 |
| Hall | C3×C13 ⋊ C2×C241 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C241 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C13×C241 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C241 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C13×C241 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9399 |
9399 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C13×D241, D3×D13×C241, D3×D3133, … |
| maximal normal subgroup of | D3×C13×D241, D3×D13×C241, D3×D3133, … |
| maximal quotient of | Dic3×C13×C241, C2×D3×C13×C241 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18798, 9);