Finite Group DatabasebetaFinite Group Databasebeta| order | 15582 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C53 · Schur multiplier (H2) = C1 |
| direct product | C7×D21×C53 |
| unambiguous semidirect product | C3⋊(C7×D7×C53) |
| unambiguous semidirect product | C7⋊(D3×C7×C53) |
| Fitting, socle, Hall | C3×C72×C53 ⋊ C2 |
| derived | C3×C7 ⋊ C2×C7×C53 |
| Hall | C72×C53 ⋊ D3 |
| Hall | C3×C53 ⋊ C7×D7 |
| Hall | C3×C72 ⋊ C2×C53 |
| Sylow | C72 ⋊ D3×C53 |
| Sylow | C3 ⋊ C7×D7×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C53 | D21 |
| commutator, cosocle, hypocenter | C3×C7 | C2×C7×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C53 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C7×C53 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2226 |
4452 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D21×D53, D3×C7×D7×C53, C7×D21⋊D53, … |
| maximal normal subgroup of | C7×D21×D53, D3×C7×D7×C53, C7×D21⋊D53, … |
| maximal quotient of | C7×C53×Dic21, C2×C7×D21×C53 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15582, 39);