Finite Group DatabasebetaFinite Group Databasebeta| order | 29526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D399 |
| unambiguous semidirect product | C3⋊(C37×D133) |
| unambiguous semidirect product | C7⋊(C37×D57) |
| unambiguous semidirect product | C19⋊(C37×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D399 |
| commutator, cosocle, hypocenter | C3×C7×C19 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C19×C37 | C2 |
| LCS | G ▷ C3×C7×C19 | |
| UCS | C1 ◁ C37 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14763 |
7437 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29526, 28);