Finite Group DatabasebetaFinite Group Databasebeta| order | 8460 |
| automorphism | Aut(G) order 4669920 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4230 |
| direct product | C2×D2115 |
| unambiguous semidirect product | (C2×C5)⋊D423 |
| unambiguous semidirect product | (C2×C9)⋊D235 |
| unambiguous semidirect product | (C2×C47)⋊D45 |
| Fitting | C2×C5×C9×C47 ⋊ C2 |
| derived, Hall | C5×C9×C47 ⋊ C22 |
| Hall | C9×C47 ⋊ C2×D5 |
| Hall | C5×C47 ⋊ C2×D9 |
| Sylow | C47 ⋊ C2×D45 |
| Hall | C5×C9 ⋊ C2×D47 |
| Sylow | C9 ⋊ C2×D235 |
| Sylow | C5 ⋊ C2×D423 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2115 |
| commutator, hypocenter | C5×C9×C47 | C22 |
| Frattini | C3 | C2×D705 |
| Fitting | C2×C5×C9×C47 | C2 |
| socle | C2×C3×C5×C47 | D3 |
| LCS | G ▷ C5×C9×C47 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
2118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8460, C2×D6345, C2×D14805 |
| maximal normal subgroup of | D8460 |
| maximal quotient of | D8460, Dic4230, C2×D6345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8460, 22);