Finite Group DatabasebetaFinite Group Databasebeta| order | 1976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C13×C19 ⋊ Q8 |
| Sylow | C19 ⋊ Dic26 |
| Sylow | C13 ⋊ Dic38 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D13×D19 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C13×C19 | C22 |
| hypocenter | C13×C19 | Q8 |
| LCS | G ▷ C2×C13×C19 ▷ C13×C19 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 1976 |
Polycyclic presentation:
2^3,13,19|a^2=c,b^2=c,b^a=bc,e^a=e^18,d^b=d^12173 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1976, 13);