Finite Group DatabasebetaFinite Group Databasebeta| order | 15582 |
| isoclinism | isoclinic class of D159 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D159 |
| unambiguous semidirect product | C3⋊(C72×D53) |
| unambiguous semidirect product | C53⋊(D3×C72) |
| Fitting, socle, Hall | C3×C72×C53 ⋊ C2 |
| derived, Hall | C3×C53 ⋊ C2×C72 |
| Hall | C72×C53 ⋊ D3 |
| Hall | C3×C72 ⋊ D53 |
| Sylow | C53 ⋊ D3×C72 |
| Sylow | C3 ⋊ C72×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D159 |
| commutator, cosocle, hypocenter | C3×C53 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C53 | C2 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C72 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7791 |
3969 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C72×D53, C7×D7×D159, C7×D21⋊D53, … |
| maximal normal subgroup of | D3×C72×D53, C7×D7×D159, C7×D21⋊D53, … |
| maximal quotient of | C72×Dic159, C2×C72×D159 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15582, 40);