Finite Group DatabasebetaFinite Group Databasebeta| order | 9842 |
| automorphism | Aut(G) order 19132848 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4921 |
| unambiguous semidirect product | C7⋊D703 |
| unambiguous semidirect product | C19⋊D259 |
| unambiguous semidirect product | C37⋊D133 |
| Fitting, socle, derived, Hall | C7×C19×C37 ⋊ C2 |
| Hall | C19×C37 ⋊ D7 |
| Hall | C7×C37 ⋊ D19 |
| Hall | C7×C19 ⋊ D37 |
| Sylow | C37 ⋊ D133 |
| Sylow | C19 ⋊ D259 |
| Sylow | C7 ⋊ D703 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C19×C37 | C2 |
| LCS | G ▷ C7×C19×C37 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,19,37|b^a=b^6,c^a=c^18,d^a=d^362462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D37×D133, D19×D259, D7×D703, … |
| maximal normal subgroup of | D37×D133, D19×D259, D7×D703, … |
| maximal quotient of | Dic4921, C2×D4921, C3×D4921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9842, 8);