Finite Group DatabasebetaFinite Group Databasebeta| order | 36708 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic483 |
| unambiguous semidirect product | C3⋊(C19×Dic161) |
| unambiguous semidirect product | C7⋊(C19×Dic69) |
| unambiguous semidirect product | C23⋊(C19×Dic21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D483 |
| commutator, hypocenter | C3×C7×C23 | C4×C19 |
| Frattini | C2 | C19×D483 |
| Fitting, socle, prime radical | C2×C3×C7×C19×C23 | C2 |
| cosocle | C2×C3×C7×C23 | C2×C19 |
| LCS | G ▷ C3×C7×C23 | |
| UCS | C1 ◁ C2×C19 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36708 |
9234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36708, 18);