Finite Group DatabasebetaFinite Group Databasebeta| order | 7638 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×D67 |
| Fitting, socle, derived, Hall | C19×C67 ⋊ C2×C3 |
| Hall | C19⋊C3×C67 ⋊ C2 |
| Hall | C19×D67 ⋊ C3 |
| Sylow | C67 ⋊ C2×C19⋊C3 |
| 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.
315 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D67, C2×C19⋊C3×D67, #37523847, … |
| maximal normal subgroup of | D19⋊C3×D67, C2×C19⋊C3×D67, #37523847, … |
| maximal quotient of | C19⋊C3×Dic67, C2×C19⋊C3×D67, D67×#4294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7638, 14);