Finite Group DatabasebetaFinite Group Databasebeta| order | 34060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C131⋊AGL(1,𝔽5) |
| Fitting, socle, Hall | C5×C13×C131 ⋊ C4 |
| derived, Hall | C5×C131 ⋊ C4×C13 |
| Hall | C13×C131 ⋊ AGL(1,𝔽5) |
| Sylow | C131 ⋊ C13×AGL(1,𝔽5) |
| Hall | C5×C13 ⋊ Dic131 |
| Sylow | C5 ⋊ C13×Dic131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C131⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C131 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C131 | C4 |
| prime radical | D5×C13×C131 | C2 |
| cosocle | D5×C131 | C2×C13 |
| LCS | G ▷ C5×C131 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8515 |
3445 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34060, 40);