Finite Group DatabasebetaFinite Group Databasebeta| order | 16785 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×C373⋊C9 |
| unambiguous semidirect product | C373⋊(C5×C9) |
| unambiguous semidirect product | (C5×C373)⋊C9 |
| derived, Sylow | C373 ⋊ C5×C9 |
| Hall | C5×C373 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C373⋊C3 |
| commutator, hypocenter | C373 | C5×C9 |
| Frattini | C3 | C5×C373⋊C3 |
| Fitting, socle, prime radical | C3×C5×C373 | C3 |
| cosocle | C3×C373 | C3×C5 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C3×C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16785 |
1905 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×C373⋊C9, C5×D373⋊C9, D5×C373⋊C9, … |
| maximal normal subgroup of | C2×C5×C373⋊C9, C5×D373⋊C9, D5×C373⋊C9, … |
| maximal quotient of | C2×C5×C373⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16785, 2);