Finite Group DatabasebetaFinite Group Databasebeta| order | 15290 |
| isoclinism | isoclinic class of D139 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×D139 |
| unambiguous semidirect product | C139⋊(C2×C5×C11) |
| Fitting, socle, Hall | C5×C11×C139 ⋊ C2 |
| derived, Sylow | C139 ⋊ C2×C5×C11 |
| Hall | C11×C139 ⋊ C2×C5 |
| Hall | C5×C139 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | D139 |
| commutator, cosocle, hypocenter | C139 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C139 | C2 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C5×C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7645 |
3905 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D11×D139, D5×C11×D139, D55×D139, … |
| maximal normal subgroup of | C5×D11×D139, D5×C11×D139, D55×D139, … |
| maximal quotient of | C5×C11×Dic139, C2×C5×C11×D139 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15290, 3);