Finite Group DatabasebetaFinite Group Databasebeta| order | 38646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C113⋊(#4294⋊C2) |
| unambiguous semidirect product | #4294⋊D113 |
| derived, Hall | C19×C113 ⋊ C2×C9 |
| Hall | C113×#4294 ⋊ C2 |
| Hall | D2147 ⋊ C9 |
| Hall | #4294 ⋊ D113 |
| Sylow | C113 ⋊ #4294⋊C2 |
| Sylow | C19 ⋊ C9×D113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C19⋊C3)⋊D113 |
| commutator, hypocenter | C19×C113 | C2×C9 |
| Fitting, socle, cosocle | C3×C19×C113 | C2×C3 |
| prime radical | C3×D2147 | C3 |
| LCS | G ▷ C19×C113 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19323 |
Polycyclic presentation:
2,3,19,113,3|b^3=e,c^a=c^18,d^a=d^112,c^b=c^71539 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38646, 12);