Finite Group DatabasebetaFinite Group Databasebeta| order | 10647 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C132 ⋊ C9 |
| Sylow | C132 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ #13095200 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #16813074 |
| commutator, hypocenter | C7×C132 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C7×C132 | C3 |
| LCS | G ▷ C7×C132 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,13^2,3|a^3=e,b^a=b^2,c^a=c^3,d^a=d^31191 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36318705, #36318708, #36318714, … |
| maximal normal subgroup of | #36318705, #36318708, #36318714, … |
| maximal quotient of | C2×#24922399 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10647, 21);