Finite Group DatabasebetaFinite Group Databasebeta| order | 7638 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊D67 |
| Fitting, socle, derived, Hall | C19×C67 ⋊ C2×C3 |
| Hall | C19⋊C3×C67 ⋊ C2 |
| Hall | D1273 ⋊ C3 |
| Sylow | C67 ⋊ D19⋊C3 |
| Hall | C19⋊C3 ⋊ D67 |
| Sylow | C19 ⋊ C3×D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C67 | C2×C3 |
| LCS | G ▷ C19×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,67|c^a=c^18,d^a=d^66,c^b=c^7306 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D67, C2×(C19⋊C3)⋊D67, #37523842, … |
| maximal normal subgroup of | D19⋊C3×D67, C2×(C19⋊C3)⋊D67, #37523842, … |
| maximal quotient of | (C19⋊C3)⋊Dic67, C2×(C19⋊C3)⋊D67, #4294⋊D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7638, 22);