Finite Group DatabasebetaFinite Group Databasebeta| order | 29610 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C47 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D21×C47 |
| unambiguous semidirect product | C3⋊(C3×C5×D7×C47) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C47 | D21 |
| commutator, cosocle, hypocenter | C3×C7 | C2×C3×C5×C47 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C47 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C3×C5×C47 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9870 |
8460 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29610, 51);