Finite Group DatabasebetaFinite Group Databasebeta| order | 7802 |
| automorphism | Aut(G) order 14714572 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3901 |
| unambiguous semidirect product | C47⋊D83 |
| unambiguous semidirect product | C83⋊D47 |
| Fitting, socle, derived, Hall | C47×C83 ⋊ C2 |
| Sylow | C83 ⋊ D47 |
| Sylow | C47 ⋊ D83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C47×C83 | C2 |
| LCS | G ▷ C47×C83 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,47,83|b^a=b^46,c^a=c^821952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×D83, C2×D3901, C3×D3901, … |
| maximal normal subgroup of | D47×D83, C2×D3901, C3×D3901 |
| maximal quotient of | Dic3901, C2×D3901, C3×D3901, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7802, 3);