Finite Group DatabasebetaFinite Group Databasebeta| order | 1368 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4294⋊C8 |
| derived, Sylow | C19 ⋊ C8×C9 |
| Hall | #4294 ⋊ C8 |
| Hall | C19⋊C8 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3×C4 | D19⋊C3 |
| commutator, hypocenter | C19 | C8×C9 |
| Fitting, cosocle | C3×C4×C19 | C2×C3 |
| socle, prime radical | C2×C3×C19 | C3×C4 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C4 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 1368 |
Polycyclic presentation:
2,3,2,3,2,19|a^2=c,b^3=d,c^2=e,f^a=f^18,f^b=f^11108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1368, 1);