Finite Group DatabasebetaFinite Group Databasebeta| order | 35340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C19×C31 | C3×C4 |
| prime radical | D5×#13183714 | C2 |
| cosocle | D5×C19×C31 | C2×C3 |
| LCS | G ▷ C5×C19×C31 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2945 |
Polycyclic presentation:
2,3,2,5,19,31|a^2=c,d^a=d^2,e^a=e^18,f^a=f^30,e^b=e^7,f^b=f^5,d^c=d^4407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35340, 113);