Finite Group DatabasebetaFinite Group Databasebeta| order | 4764 |
| automorphism | Aut(G) order 1886544 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1191 |
| unambiguous semidirect product | C3⋊Dic397 |
| derived, Hall | C3×C397 ⋊ C4 |
| Sylow | C397 ⋊ Dic3 |
| Sylow | C3 ⋊ Dic397 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1191 |
| commutator, hypocenter | C3×C397 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C397 | C2 |
| LCS | G ▷ C3×C397 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 404 |
| transitive degree | μt(G) = 4764 |
Polycyclic presentation:
2,3,397,2|a^2=d,b^a=b^2,c^a=c^3961194 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3573, C3⋊(Dic397⋊C3), C3×Dic1191, … |
| maximal normal subgroup of | C3⋊(Dic397⋊C3), C3×Dic1191, C5×Dic1191, … |
| maximal quotient of | Dic3573, C3×Dic1191, C3⋊Dic1191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4764, 6);