Finite Group DatabasebetaFinite Group Databasebeta| order | 4902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C43 ⋊ C2×C3 |
| Hall | #14578576 ⋊ C2 |
| Hall | D19×C43 ⋊ C3 |
| Sylow | C43 ⋊ D19⋊C3 |
| Hall | D19 ⋊ C43⋊C3 |
| Sylow | C19 ⋊ C2×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C43 | C2×C3 |
| LCS | G ▷ C19×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,43|c^a=c^18,c^b=c^7,d^b=d^36163 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×C43⋊C3, C3×#19096729, C3⋊#19096729, … |
| maximal normal subgroup of | D19⋊C3×C43⋊C3, C3×#19096729, C5×#19096729, … |
| maximal quotient of | #28413663, C3×#19096729, C3⋊#19096729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4902, 19);