Finite Group DatabasebetaFinite Group Databasebeta| order | 1976 |
| isoclinism | isoclinic class of C19⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C19⋊#261 |
| unambiguous semidirect product | D13⋊Dic19 |
| unambiguous semidirect product | (C2×C19)⋊#261 |
| Fitting, socle | C2×C13×C19 ⋊ C4 |
| derived, Hall | C13×C19 ⋊ C2×C4 |
| Sylow | C19 ⋊ C2×#261 |
| Sylow | C13 ⋊ C2×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C19⋊#261 |
| commutator, hypocenter | C13×C19 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C19 | C4 |
| prime radical | C2×C19×D13 | C2 |
| cosocle | C19×D13 | C22 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 494 |
158 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1976, 34);