Finite Group DatabasebetaFinite Group Databasebeta| order | 3159 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C310 |
| direct product | C34×C13⋊C3 |
| unambiguous semidirect product | C13⋊C35 |
| unambiguous semidirect product | (C3×C13)⋊C34 |
| Fitting, socle | C34×C13 ⋊ C3 |
| derived, Sylow | C13 ⋊ C35 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C34 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C35 |
| Frattini | C1 | G |
| Fitting, socle | C34×C13 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C34 | |
5328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1053 |
567 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3159, 309);