Finite Group DatabasebetaFinite Group Databasebeta| order | 30140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×Dic137 |
| derived, Sylow | C137 ⋊ C4×C5×C11 |
| Hall | C5×C11×C137 ⋊ C4 |
| Hall | C11×C137 ⋊ C4×C5 |
| Hall | C5×C137 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C11 | D137 |
| commutator, hypocenter | C137 | C4×C5×C11 |
| Frattini | C2 | C5×C11×D137 |
| Fitting, socle, prime radical | C2×C5×C11×C137 | C2 |
| cosocle | C2×C137 | C2×C5×C11 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C5×C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30140 |
7700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30140, 3);