Finite Group DatabasebetaFinite Group Databasebeta| order | 30140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D55⋊D137 |
| unambiguous semidirect product | D685⋊D11 |
| unambiguous semidirect product | D1507⋊D5 |
| Fitting, socle, derived, Hall | C5×C11×C137 ⋊ C22 |
| Hall | C11×C137 ⋊ C2×D5 |
| Hall | C5×C137 ⋊ C2×D11 |
| Sylow | C137 ⋊ D5×D11 |
| Hall | C5×C11 ⋊ C2×D137 |
| Sylow | C11 ⋊ D5×D137 |
| Sylow | C5 ⋊ D11×D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C137 | C22 |
| LCS | G ▷ C5×C11×C137 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7535 |
Polycyclic presentation:
2^2,5,11,137|d^a=d^10,e^a=e^136,c^b=c^4,d^b=d^102000 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30140, 39);