Finite Group DatabasebetaFinite Group Databasebeta| order | 9804 |
| automorphism | Aut(G) order 7411824 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4902 |
| direct product | C2×D2451 |
| unambiguous semidirect product | (C2×C3)⋊D817 |
| unambiguous semidirect product | (C2×C19)⋊D129 |
| unambiguous semidirect product | (C2×C43)⋊D57 |
| Fitting, socle | C2×C3×C19×C43 ⋊ C2 |
| derived, Hall | C3×C19×C43 ⋊ C22 |
| Hall | C19×C43 ⋊ C2×D3 |
| Hall | C3×C43 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×D57 |
| Sylow | C19 ⋊ C2×D129 |
| Sylow | C3 ⋊ C2×D817 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2451 |
| commutator, cosocle, hypocenter | C3×C19×C43 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C19×C43 | C2 |
| LCS | G ▷ C3×C19×C43 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2454 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9804, 58);