Finite Group DatabasebetaFinite Group Databasebeta| order | 4516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1129 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1129 | C4 |
| prime radical, cosocle | D1129 | C2 |
| LCS | G ▷ C1129 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1129 |
| transitive degree | μt(G) = 1129 |
Polycyclic presentation:
2^2,1129|a^2=b,c^a=c^168,c^b=c^1128286 conjugacy classes — view the full character table.
| maximal subgroup of | #17985266⋊C3, C3×#17985266, C3⋊#17985266, … |
| maximal normal subgroup of | #17985266⋊C3, C3×#17985266, C5×#17985266, … |
| maximal quotient of | C3×#17985266, C3⋊#17985266, C5×#17985266, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4516, 3);