Finite Group DatabasebetaFinite Group Databasebeta| order | 4514 |
| automorphism | Aut(G) order 4875120 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2257 |
| unambiguous semidirect product | C37⋊D61 |
| unambiguous semidirect product | C61⋊D37 |
| Fitting, socle, derived, Hall | C37×C61 ⋊ C2 |
| Sylow | C61 ⋊ D37 |
| Sylow | C37 ⋊ D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C61 | C2 |
| LCS | G ▷ C37×C61 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 98 |
| transitive degree | μt(G) = 2257 |
Polycyclic presentation:
2,37,61|b^a=b^36,c^a=c^601130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2257, D6771, (C61⋊C3)⋊D37, … |
| maximal normal subgroup of | C3×D2257, (C61⋊C3)⋊D37, (C37⋊C3)⋊D61, … |
| maximal quotient of | C3×D2257, D6771, C5×D2257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4514, 3);