Finite Group DatabasebetaFinite Group Databasebeta| order | 16770 |
| isoclinism | isoclinic class of D43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C5×C13×D43⋊C3 |
| unambiguous semidirect product | D43⋊(C3×C5×C13) |
| unambiguous semidirect product | (C43⋊C3)⋊(C2×C5×C13) |
| unambiguous semidirect product | (C5×D43)⋊(C3×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C13 | D43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C2×C3×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C43 | C2×C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C5×C13 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2795 |
845 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D13×D43⋊C3, D5×C13×D43⋊C3, D65×D43⋊C3, … |
| maximal normal subgroup of | C5×D13×D43⋊C3, D5×C13×D43⋊C3, D65×D43⋊C3, … |
| maximal quotient of | C5×C13×(C43⋊C3)⋊C4, C2×C5×C13×D43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16770, 21);