Finite Group DatabasebetaFinite Group Databasebeta| order | 10386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19104460⋊C2 |
| derived, Sylow | C577 ⋊ C2×C9 |
| Hall | #19104460 ⋊ C2 |
| Hall | D577 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D577⋊C3 |
| commutator, hypocenter | C577 | C2×C9 |
| Fitting, socle, cosocle | C3×C577 | C2×C3 |
| prime radical | C3×D577 | C3 |
| LCS | G ▷ C577 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,577,3|b^3=d,c^a=c^576,c^b=c^363306 conjugacy classes — view the full character table.
| maximal subgroup of | #35209364, C2×#19104460⋊C2 |
| maximal normal subgroup of | #35209364, C2×#19104460⋊C2 |
| maximal quotient of | #35209358, C2×#19104460⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10386, 2);