Finite Group DatabasebetaFinite Group Databasebeta| order | 9460 |
| automorphism | Aut(G) order 7946400 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4730 |
| direct product | C2×D2365 |
| unambiguous semidirect product | (C2×C5)⋊D473 |
| unambiguous semidirect product | (C2×C11)⋊D215 |
| unambiguous semidirect product | (C2×C43)⋊D55 |
| Fitting, socle | C2×C5×C11×C43 ⋊ C2 |
| derived, Hall | C5×C11×C43 ⋊ C22 |
| Hall | C11×C43 ⋊ C2×D5 |
| Hall | C5×C43 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×D55 |
| Sylow | C11 ⋊ C2×D215 |
| Sylow | C5 ⋊ C2×D473 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2365 |
| commutator, hypocenter | C5×C11×C43 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C11×C43 | C2 |
| LCS | G ▷ C5×C11×C43 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5⋊(C11⋊(D43⋊C3)), D3×D2365, C2×C3×D2365, … |
| maximal normal subgroup of | C2×C5⋊(C11⋊(D43⋊C3)), C2×C3×D2365, D9460 |
| maximal quotient of | D3×D2365, C2×C3×D2365, C2×D7095, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9460, 30);