Finite Group DatabasebetaFinite Group Databasebeta| order | 10647 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C169 ⋊ C9 |
| Sylow | C169 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ C169⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16813063 |
| commutator, hypocenter | C7×C169 | C9 |
| Frattini | C3×C13 | #63270 |
| Fitting, cosocle | C3×C7×C169 | C3 |
| socle, prime radical | C3×C7×C13 | C13⋊C3 |
| LCS | G ▷ C7×C169 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,13,3,13|a^3=d,c^13=e^6,b^a=b^2,c^a=c^3e,e^a=e^31191 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36318614, #36318618, #36318620, … |
| maximal normal subgroup of | #36318614, #36318618, #36318620, … |
| maximal quotient of | C2×#24922382 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10647, 4);