Finite Group DatabasebetaFinite Group Databasebeta| order | 30140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊#10587739 |
| unambiguous semidirect product | (C11⋊#10587739)⋊C5 |
| Fitting, socle, derived, Hall | C11×C137 ⋊ C4×C5 |
| Hall | C11⋊C5×C137 ⋊ C4 |
| Hall | C11⋊#10587739 ⋊ C5 |
| Sylow | C137 ⋊ Dic11⋊C5 |
| Hall | C11⋊C5 ⋊ #10587739 |
| Sylow | C11 ⋊ C5×#10587739 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C137 | C4×C5 |
| prime radical | C11⋊C5×D137 | C2 |
| cosocle | C11×D137 | C2×C5 |
| LCS | G ▷ C11×C137 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1507 |
Polycyclic presentation:
2,5,2,11,137|a^2=c,d^a=d^10,e^a=e^100,d^b=d^4,e^c=e^136260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30140, 14);