Finite Group DatabasebetaFinite Group Databasebeta| order | 1292 |
| isoclinism | isoclinic class of C19⋊#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#595 |
| Fitting, socle, derived, Hall | C17×C19 ⋊ C4 |
| Sylow | C19 ⋊ #595 |
| Sylow | C17 ⋊ Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C19 | C4 |
| prime radical, cosocle | C19×D17 | C2 |
| LCS | G ▷ C17×C19 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 323 |
Polycyclic presentation:
2^2,17,19|a^2=b,c^a=c^13,d^a=d^18,c^b=c^1698 conjugacy classes — view the full character table.
| maximal subgroup of | (C19⋊C3)⋊#595, C3×C19⋊#595, C3⋊(C19⋊#595), … |
| maximal normal subgroup of | (C19⋊C3)⋊#595, C3×C19⋊#595, C11×C19⋊#595, … |
| maximal quotient of | C3×C19⋊#595, C3⋊(C19⋊#595), C19⋊#10597479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1292, 6);