Finite Group DatabasebetaFinite Group Databasebeta| order | 7638 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C67 ⋊ C2×C3 |
| Hall | #16838390 ⋊ C2 |
| Hall | D19×C67 ⋊ C3 |
| Sylow | C67 ⋊ D19⋊C3 |
| Hall | D19 ⋊ C67⋊C3 |
| Sylow | C19 ⋊ C2×C67⋊C3 |
| 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,c^b=c^7,d^b=d^37251 conjugacy classes — view the full character table.
| maximal subgroup of | #21439405⋊C2, C2×#21439409, D19⋊C3×C67⋊C3, … |
| maximal normal subgroup of | #21439405⋊C2, C2×#21439409, D19⋊C3×C67⋊C3, … |
| maximal quotient of | #29504133, C2×#21439409, #37523834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7638, 19);