Finite Group DatabasebetaFinite Group Databasebeta| order | 10038 |
| automorphism | Aut(G) order 14334264 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5019 |
| unambiguous semidirect product | C3⋊D1673 |
| unambiguous semidirect product | C7⋊D717 |
| unambiguous semidirect product | C239⋊D21 |
| Fitting, socle, derived, Hall | C3×C7×C239 ⋊ C2 |
| Hall | C7×C239 ⋊ D3 |
| Hall | C3×C239 ⋊ D7 |
| Sylow | C239 ⋊ D21 |
| Hall | C3×C7 ⋊ D239 |
| Sylow | C7 ⋊ D717 |
| Sylow | C3 ⋊ D1673 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C239 | C2 |
| LCS | G ▷ C3×C7×C239 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,239|b^a=b^2,c^a=c^6,d^a=d^2382511 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D21×D239, D7×D717, D3×D1673, … |
| maximal normal subgroup of | D21×D239, D7×D717, D3×D1673, … |
| maximal quotient of | Dic5019, C2×D5019, D15057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10038, 10);