Finite Group DatabasebetaFinite Group Databasebeta| order | 4902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊D43 |
| Fitting, socle, derived, Hall | C19×C43 ⋊ C2×C3 |
| Hall | C43×C19⋊C3 ⋊ C2 |
| Hall | D817 ⋊ C3 |
| Hall | C19⋊C3 ⋊ D43 |
| Sylow | C43 ⋊ D19⋊C3 |
| Sylow | C19 ⋊ C3×D43 |
| 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,d^a=d^42,c^b=c^7198 conjugacy classes — view the full character table.
| maximal subgroup of | #28413671, #28413672, #4296⋊D43, … |
| maximal normal subgroup of | #28413671, #28413672, #4296⋊D43, … |
| maximal quotient of | #4294⋊D43, C3×(C19⋊C3)⋊D43, C3⋊((C19⋊C3)⋊D43), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4902, 22);