Finite Group DatabasebetaFinite Group Databasebeta| order | 10386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#19104460 |
| derived, Sylow | C577 ⋊ C2×C9 |
| Hall | C2×C577 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C577⋊C3 |
| commutator, hypocenter | C577 | C2×C9 |
| Frattini | C3 | C2×C577⋊C3 |
| Fitting, socle, prime radical | C2×C3×C577 | C3 |
| cosocle | C3×C577 | C2×C3 |
| LCS | G ▷ C577 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
1170 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35209358, C4×#19104460, C2×#19104460⋊C2, … |
| maximal normal subgroup of | #35209358, C4×#19104460, C2×#19104460⋊C2, … |
| maximal quotient of | C4×#19104460, C22×#19104460 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10386, 3);