Finite Group DatabasebetaFinite Group Databasebeta| order | 4902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×D43 |
| Fitting, socle, derived, Hall | C19×C43 ⋊ C2×C3 |
| Hall | C43×C19⋊C3 ⋊ C2 |
| Hall | C19×D43 ⋊ C3 |
| Sylow | C43 ⋊ C2×C19⋊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.
207 conjugacy classes — view the full character table.
| maximal subgroup of | #28413676, #28413677, D43×#4296, … |
| maximal normal subgroup of | #28413676, #28413677, D43×#4296, … |
| maximal quotient of | D43×#4294, C3×C19⋊C3×D43, C19⋊C3×D129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4902, 14);