Finite Group DatabasebetaFinite Group Databasebeta| order | 1976 |
| isoclinism | isoclinic class of D13×D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C13×C19 ⋊ C2×C4 |
| Sylow | C19 ⋊ C4×D13 |
| Sylow | C13 ⋊ C4×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D13×D19 |
| commutator, hypocenter | C13×C19 | C2×C4 |
| Fitting, socle, cosocle | C2×C13×C19 | C22 |
| prime radical | C2×D247 | C2 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 988 |
Polycyclic presentation:
2^3,13,19|a^2=c,b^2=c,e^a=e^18,d^b=d^12176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1976, 9);