Finite Group DatabasebetaFinite Group Databasebeta| order | 34060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C131⋊#63122 |
| Fitting, socle, derived, Hall | C5×C13×C131 ⋊ C4 |
| Hall | C13×C131 ⋊ AGL(1,𝔽5) |
| Hall | C5×C131 ⋊ #261 |
| Sylow | C131 ⋊ #63122 |
| Hall | C5×C13 ⋊ Dic131 |
| Sylow | C13 ⋊ C131⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C131⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C131 | C4 |
| prime radical, cosocle | D65×C131 | C2 |
| LCS | G ▷ C5×C13×C131 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8515 |
Polycyclic presentation:
2^2,5,13,131|a^2=b,c^a=c^2,d^a=d^5,e^a=e^130,c^b=c^4,d^b=d^122230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34060, 42);