Finite Group DatabasebetaFinite Group Databasebeta| order | 3516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#11924078 |
| Fitting, socle, derived, Hall | C3×C293 ⋊ C4 |
| Sylow | C293 ⋊ Dic3 |
| Sylow | C3 ⋊ #11924078 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C293 | C4 |
| prime radical, cosocle | C3×D293 | C2 |
| LCS | G ▷ C3×C293 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 296 |
| transitive degree | μt(G) = 879 |
Polycyclic presentation:
2^2,3,293|a^2=b,c^a=c^2,d^a=d^138,d^b=d^292225 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C3⋊#11924078, C3⋊#19154443, C3⋊#19154444, … |
| maximal normal subgroup of | C5×C3⋊#11924078, C7×C3⋊#11924078 |
| maximal quotient of | C5×C3⋊#11924078, C3⋊#19154443, C3⋊#19154444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3516, 7);