Finite Group DatabasebetaFinite Group Databasebeta| order | 38646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C19⋊C3×D113 |
| unambiguous semidirect product | C113⋊(C2×C3×C19⋊C3) |
| unambiguous semidirect product | (C19×D113)⋊C32 |
| unambiguous semidirect product | (C3×C19×D113)⋊C3 |
| Fitting, socle | C3×C19×C113 ⋊ C2×C3 |
| derived, Hall | C19×C113 ⋊ C2×C32 |
| Hall | C3×C19⋊C3×C113 ⋊ C2 |
| Hall | C19×D113 ⋊ C32 |
| Sylow | C113 ⋊ C2×C3×C19⋊C3 |
| Sylow | C19 ⋊ C32×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C19⋊C3×D113 |
| commutator, cosocle, hypocenter | C19×C113 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C113 | C2×C3 |
| LCS | G ▷ C19×C113 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6441 |
1566 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38646, 20);