Finite Group DatabasebetaFinite Group Databasebeta| order | 7638 |
| automorphism | Aut(G) order 9073944 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3819 |
| unambiguous semidirect product | C3⋊D1273 |
| unambiguous semidirect product | C19⋊D201 |
| unambiguous semidirect product | C67⋊D57 |
| Fitting, socle, derived, Hall | C3×C19×C67 ⋊ C2 |
| Hall | C19×C67 ⋊ D3 |
| Hall | C3×C67 ⋊ D19 |
| Sylow | C67 ⋊ D57 |
| Hall | C3×C19 ⋊ D67 |
| Sylow | C19 ⋊ D201 |
| Sylow | C3 ⋊ D1273 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C19×C67 | C2 |
| LCS | G ▷ C3×C19×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,67|b^a=b^2,c^a=c^18,d^a=d^661911 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D57×D67, D19×D201, D3×D1273, … |
| maximal normal subgroup of | D57×D67, D19×D201, D3×D1273, … |
| maximal quotient of | Dic3819, C2×D3819, D11457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7638, 12);