Finite Group DatabasebetaFinite Group Databasebeta| order | 1976 |
| isoclinism | isoclinic class of D247 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#1055 |
| derived, Hall | C13×C19 ⋊ C8 |
| Sylow | C19 ⋊ #1055 |
| Sylow | C13 ⋊ C19⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D247 |
| commutator, hypocenter | C13×C19 | C8 |
| Fitting, cosocle | C4×C13×C19 | C2 |
| socle, prime radical | C2×C13×C19 | C4 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 1976 |
Polycyclic presentation:
2^3,13,19|a^2=b,b^2=c,d^a=d^12,e^a=e^18500 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1976, 3);