Finite Group DatabasebetaFinite Group Databasebeta| order | 37278 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C109 ⋊ C2×C9 |
| Hall | #32916125 ⋊ C2 |
| Hall | D19×C109 ⋊ C9 |
| Sylow | C109 ⋊ AGL(1,𝔽19) |
| Hall | D19 ⋊ #11758279 |
| Sylow | C19 ⋊ C2×#11758279 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C109 | C2×C9 |
| prime radical | C109×D19⋊C3 | C3 |
| cosocle | C19⋊C3×C109 | C2×C3 |
| LCS | G ▷ C19×C109 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2071 |
Polycyclic presentation:
2,3^2,19,109|b^3=c,d^a=d^18,d^b=d^4,e^b=e^63,d^c=d^7343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37278, 42);