Finite Group DatabasebetaFinite Group Databasebeta| order | 10647 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#11717942 |
| derived | C7×C13 ⋊ C9×C13 |
| Hall | C7×C132 ⋊ C9 |
| Sylow | C132 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ C13×C13⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | #63271 |
| commutator, hypocenter | C7×C13 | C9×C13 |
| Frattini | C3 | C13×#63271 |
| Fitting, socle, prime radical | C3×C7×C132 | C3 |
| cosocle | C3×C7×C13 | C3×C13 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3×C13 | |
40 conjugacy classes of subgroups.
1287 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×#13109903, C13×#13109901, #36318713, … |
| maximal normal subgroup of | C13×#13109903, C13×#13109901, #36318713, … |
| maximal quotient of | C2×C13×#11717942 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10647, 20);