Finite Group DatabasebetaFinite Group Databasebeta| order | 4794 |
| automorphism | Aut(G) order 3528384 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2397 |
| unambiguous semidirect product | C3⋊D799 |
| unambiguous semidirect product | C17⋊D141 |
| unambiguous semidirect product | C47⋊D51 |
| Fitting, socle, derived, Hall | C3×C17×C47 ⋊ C2 |
| Hall | C17×C47 ⋊ D3 |
| Hall | C3×C47 ⋊ D17 |
| Hall | C3×C17 ⋊ D47 |
| Sylow | C47 ⋊ D51 |
| Sylow | C17 ⋊ D141 |
| Sylow | C3 ⋊ D799 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C47 | C2 |
| LCS | G ▷ C3×C17×C47 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2397 |
Polycyclic presentation:
2,3,17,47|b^a=b^2,c^a=c^16,d^a=d^461200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7191, C3⋊D2397, C3×D2397, … |
| maximal normal subgroup of | C3×D2397, C5×D2397, C7×D2397 |
| maximal quotient of | D7191, C3⋊D2397, C3×D2397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4794, 8);