Finite Group DatabasebetaFinite Group Databasebeta| order | 4516 |
| automorphism | Aut(G) order 2547024 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1129 |
| derived, Sylow | C1129 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1129 |
| commutator, hypocenter | C1129 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C1129 | C2 |
| LCS | G ▷ C1129 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1133 |
| transitive degree | μt(G) = 4516 |
Polycyclic presentation:
2^2,1129|a^2=b,c^a=c^11281132 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic1129⋊C3, C3×Dic1129, Dic3387, … |
| maximal normal subgroup of | Dic1129⋊C3, C3×Dic1129, C5×Dic1129, … |
| maximal quotient of | C3×Dic1129, Dic3387, C5×Dic1129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4516, 1);