Finite Group DatabasebetaFinite Group Databasebeta| order | 34650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C7×C11 · Schur multiplier (H2) = C3×C5 |
| direct product | C52×C7×C11×C3⋊D3 |
| unambiguous semidirect product | C3⋊(C52×D3×C7×C11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C7×C11 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C2×C52×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C7×C11 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C52×C7×C11 | |
384 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17325 |
11550 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34650, 317);