Finite Group DatabasebetaFinite Group Databasebeta| order | 16770 |
| isoclinism | isoclinic class of C5⋊(D13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×C5⋊(D13⋊C3) |
| unambiguous semidirect product | C5⋊(C43×D13⋊C3) |
| unambiguous semidirect product | (C13⋊C3)⋊(D5×C43) |
| unambiguous semidirect product | D65⋊(C3×C43) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C5⋊(D13⋊C3) |
| commutator, cosocle, hypocenter | C5×C13 | C2×C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C43 | C2×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C43 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2795 |
946 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#63122⋊C3, #46776449, C43×#63121⋊C3, … |
| maximal normal subgroup of | C43×#63122⋊C3, #46776449, C43×#63121⋊C3, … |
| maximal quotient of | C43×Dic65⋊C3, C2×C43×C5⋊(D13⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16770, 42);