Finite Group DatabasebetaFinite Group Databasebeta| order | 35340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D19×(C31⋊C3)⋊C5 |
| unambiguous semidirect product | (C2×D19×C31⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D19×(C31⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C19×C31 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C31 | C2×C3×C5 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1178 |
374 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35340, 89);