Finite Group DatabasebetaFinite Group Databasebeta| order | 15582 |
| isoclinism | isoclinic class of D49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D49⋊C3 |
| unambiguous semidirect product | D49⋊(C3×C53) |
| unambiguous semidirect product | (C49⋊C3)⋊(C2×C53) |
| unambiguous semidirect product | (C53×D49)⋊C3 |
| Fitting, Hall | C49×C53 ⋊ C2×C3 |
| derived, Sylow | C49 ⋊ C2×C3×C53 |
| Hall | C53×C49⋊C3 ⋊ C2 |
| Hall | C53×D49 ⋊ C3 |
| Hall | C49⋊C3 ⋊ C2×C53 |
| Hall | D49 ⋊ C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C2×C3×C53 |
| Frattini | C7 | AGL(1,𝔽7)×C53 |
| Fitting | C49×C53 | C2×C3 |
| socle | C7×C53 | AGL(1,𝔽7) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C53 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2597 |
742 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×D49⋊C3, C2×C53×D49⋊C3 |
| maximal normal subgroup of | D53×D49⋊C3, C2×C53×D49⋊C3 |
| maximal quotient of | C53×(C49⋊C3)⋊C4, C2×C53×D49⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15582, 11);