Finite Group DatabasebetaFinite Group Databasebeta| order | 4902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D817 |
| Fitting, socle, Hall | C3×C19×C43 ⋊ C2 |
| derived, Hall | C19×C43 ⋊ C2×C3 |
| Hall | C3×C43 ⋊ D19 |
| Hall | C3×C19 ⋊ D43 |
| Sylow | C43 ⋊ C3×D19 |
| Sylow | C19 ⋊ C3×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D817 |
| commutator, hypocenter | C19×C43 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C43 | C2 |
| LCS | G ▷ C19×C43 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
1230 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D817, (C43⋊C9)⋊D19, #4294⋊D43, … |
| maximal normal subgroup of | C9×D817, (C43⋊C9)⋊D19, #4294⋊D43, … |
| maximal quotient of | C9×D817, C3×D2451, C32×D817, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4902, 8);