Finite Group DatabasebetaFinite Group Databasebeta| order | 34650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C7⋊#90646 |
| unambiguous semidirect product | C7⋊(C11×#90646) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C7⋊#90646 |
| commutator, cosocle, hypocenter | C7×C52⋊C9 | C2×C11 |
| Frattini | C3 | C11×C7⋊#3874 |
| Fitting, socle | C3×C52×C7×C11 | D3 |
| LCS | G ▷ C7×C52⋊C9 | |
| UCS | C1 ◁ C11 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3465 |
1353 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34650, 134);