Finite Group DatabasebetaFinite Group Databasebeta| order | 3196 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊#595 |
| Fitting, socle, derived, Hall | C17×C47 ⋊ C4 |
| Sylow | C47 ⋊ #595 |
| Sylow | C17 ⋊ Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C47 | C4 |
| prime radical, cosocle | D17×C47 | C2 |
| LCS | G ▷ C17×C47 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 799 |
Polycyclic presentation:
2^2,17,47|a^2=b,c^a=c^13,d^a=d^46,c^b=c^16238 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C47⋊#595, C47⋊#66775, C47⋊#66776, … |
| maximal normal subgroup of | C5×C47⋊#595, C7×C47⋊#595, C11×C47⋊#595 |
| maximal quotient of | C5×C47⋊#595, C47⋊#66775, C47⋊#66776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3196, 7);