Finite Group DatabasebetaFinite Group Databasebeta| order | 17838 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #22581943⋊C2 |
| derived, Sylow | C991 ⋊ C2×C9 |
| Hall | #22581943 ⋊ C2 |
| Hall | D991 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D991⋊C3 |
| commutator, hypocenter | C991 | C2×C9 |
| Fitting, socle, cosocle | C3×C991 | C2×C3 |
| prime radical | C3×D991 | C3 |
| LCS | G ▷ C991 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8919 |
Polycyclic presentation:
2,3,991,3|b^3=d,c^a=c^990,c^b=c^113513 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22581943⋊C2 |
| maximal normal subgroup of | C2×#22581943⋊C2 |
| maximal quotient of | #22581943⋊C4, C2×#22581943⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17838, 2);