Finite Group DatabasebetaFinite Group Databasebeta| order | 4516 |
| automorphism | Aut(G) order 2547024 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2258 |
| direct product | C2×D1129 |
| unambiguous semidirect product | C1129⋊C22 |
| unambiguous semidirect product | (C2×C1129)⋊C2 |
| Fitting, socle | C2×C1129 ⋊ C2 |
| derived, Sylow | C1129 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1129 |
| commutator, cosocle, hypocenter | C1129 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1129 | C2 |
| LCS | G ▷ C1129 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2258 |
1132 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D1129⋊C3, D3×D1129, C2×D3387, … |
| maximal normal subgroup of | C2×D1129⋊C3, C2×C3×D1129, C2×C5×D1129, … |
| maximal quotient of | D3×D1129, C2×D3387, C2×C3×D1129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4516, 4);