Finite Group DatabasebetaFinite Group Databasebeta| order | 7730 |
| automorphism | Aut(G) order 11935120 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3865 |
| unambiguous semidirect product | C5⋊D773 |
| unambiguous semidirect product | C773⋊D5 |
| Fitting, socle, derived, Hall | C5×C773 ⋊ C2 |
| Sylow | C773 ⋊ D5 |
| Sylow | C5 ⋊ D773 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C773 | C2 |
| LCS | G ▷ C5×C773 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,773|b^a=b^4,c^a=c^7721934 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29509036, #29509037, D5×D773, … |
| maximal normal subgroup of | #29509036, #29509037, D5×D773, … |
| maximal quotient of | Dic3865, C2×D3865, C3×D3865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7730, 3);