Finite Group DatabasebetaFinite Group Databasebeta| order | 15738 |
| isoclinism | isoclinic class of D43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D43⋊C3 |
| unambiguous semidirect product | D43⋊(C3×C61) |
| unambiguous semidirect product | (C43⋊C3)⋊(C2×C61) |
| Fitting, socle, Hall | C43×C61 ⋊ C2×C3 |
| derived, Sylow | C43 ⋊ C2×C3×C61 |
| Hall | C61×C43⋊C3 ⋊ C2 |
| Hall | C61×D43 ⋊ C3 |
| Hall | C43⋊C3 ⋊ C2×C61 |
| Hall | D43 ⋊ C3×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C2×C3×C61 |
| Frattini | C1 | G |
| Fitting, socle | C43×C61 | C2×C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C61 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2623 |
793 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×D43⋊C3, C2×C61×D43⋊C3 |
| maximal normal subgroup of | D61×D43⋊C3, C2×C61×D43⋊C3 |
| maximal quotient of | C61×(C43⋊C3)⋊C4, C2×C61×D43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15738, 18);