Finite Group DatabasebetaFinite Group Databasebeta| order | 16770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C43⋊C3×D65 |
| unambiguous semidirect product | C5⋊(D13×C43⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C13×C43 | C2×C3 |
| LCS | G ▷ C5×C13×C43 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2795 |
578 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C43⋊C3)⋊#63122, C43⋊C3×#63122, (C43⋊C3)⋊#63121, … |
| maximal normal subgroup of | (C43⋊C3)⋊#63122, C43⋊C3×#63122, (C43⋊C3)⋊#63121, … |
| maximal quotient of | C43⋊C3×Dic65, C2×C43⋊C3×D65 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16770, 41);