Finite Group DatabasebetaFinite Group Databasebeta| order | 10647 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#13095200 |
| derived, Sylow | C132 ⋊ C7×C9 |
| Hall | C7×C132 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | #92788 |
| commutator, hypocenter | C132 | C7×C9 |
| Frattini | C3 | C7×#92788 |
| Fitting, socle, prime radical | C3×C7×C132 | C3 |
| cosocle | C3×C132 | C3×C7 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C3×C7 | |
96 conjugacy classes of subgroups.
1239 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#15690148, C7×#15690150, #36318737, … |
| maximal normal subgroup of | C7×#15690148, C7×#15690150, #36318737, … |
| maximal quotient of | C2×C7×#13095200 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10647, 16);