Finite Group DatabasebetaFinite Group Databasebeta| order | 30140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#14582305 |
| Fitting, socle, derived, Hall | C5×C11×C137 ⋊ C4 |
| Hall | C11×C137 ⋊ AGL(1,𝔽5) |
| Hall | C5×C137 ⋊ Dic11 |
| Sylow | C137 ⋊ C11⋊AGL(1,𝔽5) |
| Hall | C5×C11 ⋊ Dic137 |
| Sylow | C11 ⋊ #14582305 |
| Sylow | C5 ⋊ Dic1507 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C11×C137 | C4 |
| prime radical, cosocle | D5×C11×C137 | C2 |
| LCS | G ▷ C5×C11×C137 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7535 |
Polycyclic presentation:
2^2,5,11,137|a^2=b,c^a=c^2,d^a=d^10,e^a=e^136,c^b=c^43017 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30140, 31);