Finite Group DatabasebetaFinite Group Databasebeta| order | 36290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C2×(C191⋊C5)⋊C19 |
| unambiguous semidirect product | (C2×C191⋊C5)⋊C19 |
| unambiguous semidirect product | (C2×C191⋊C19)⋊C5 |
| Fitting, socle, Hall | C2×C191 ⋊ C5×C19 |
| derived, Sylow | C191 ⋊ C2×C5×C19 |
| Hall | C2×C191⋊C19 ⋊ C5 |
| Hall | C191⋊C19 ⋊ C2×C5 |
| Hall | C2×C191⋊C5 ⋊ C19 |
| Hall | C191⋊C5 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C191⋊C5)⋊C19 |
| commutator, cosocle, hypocenter | C191 | C2×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C191 | C5×C19 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
194 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36290, 4);