Finite Group DatabasebetaFinite Group Databasebeta| order | 3516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#11924078 |
| Fitting, socle, Hall | C3×C293 ⋊ C4 |
| derived, Sylow | C293 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11924078 |
| commutator, hypocenter | C293 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C293 | C4 |
| prime radical | C3×D293 | C2 |
| cosocle | D293 | C2×C3 |
| LCS | G ▷ C293 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 296 |
| transitive degree | μt(G) = 879 |
231 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×#11924078, C3×#19154443, C3×#19154444, … |
| maximal normal subgroup of | C3×C5×#11924078, C3×C7×#11924078 |
| maximal quotient of | C3×C5×#11924078, C3×#19154443, C3×#19154444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3516, 6);