Finite Group DatabasebetaFinite Group Databasebeta| order | 37278 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×C3⋊(D109⋊C3) |
| unambiguous semidirect product | C3⋊(C19×D109⋊C3) |
| unambiguous semidirect product | (C109⋊C3)⋊(D3×C19) |
| unambiguous semidirect product | D327⋊(C3×C19) |
| Fitting, socle | C3×C19×C109 ⋊ C2×C3 |
| derived | C3×C109 ⋊ C2×C3×C19 |
| Hall | C3×C19×C109⋊C3 ⋊ C2 |
| Hall | C19×C109 ⋊ C3×D3 |
| Hall | C3×C109⋊C3 ⋊ C2×C19 |
| Sylow | C109 ⋊ C3×D3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C3⋊(D109⋊C3) |
| commutator, cosocle, hypocenter | C3×C109 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C109 | C2×C3 |
| LCS | G ▷ C3×C109 | |
| UCS | C1 ◁ C19 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6213 |
1197 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37278, 90);