Finite Group DatabasebetaFinite Group Databasebeta| order | 4542 |
| automorphism | Aut(G) order 3433752 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2271 |
| unambiguous semidirect product | C3⋊D757 |
| unambiguous semidirect product | C757⋊D3 |
| Fitting, socle, derived, Hall | C3×C757 ⋊ C2 |
| Sylow | C757 ⋊ D3 |
| Sylow | C3 ⋊ D757 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C757 | C2 |
| LCS | G ▷ C3×C757 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 760 |
| transitive degree | μt(G) = 2271 |
Polycyclic presentation:
2,3,757|b^a=b^2,c^a=c^7561137 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D6813, C3⋊(D757⋊C3), C3⋊D2271, … |
| maximal normal subgroup of | C3⋊(D757⋊C3), C3×D2271, C5×D2271, … |
| maximal quotient of | D6813, C3⋊D2271, C3×D2271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4542, 5);