Finite Group DatabasebetaFinite Group Databasebeta| order | 8643 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C43×C67 ⋊ C3 |
| Sylow | C67 ⋊ C43⋊C3 |
| Sylow | C43 ⋊ C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C43×C67 | C3 |
| LCS | G ▷ C43×C67 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,43,67|b^a=b^6,c^a=c^29963 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22575686, #31772250, #31772254, … |
| maximal normal subgroup of | C2×#22575686, #31772250, #31772254, … |
| maximal quotient of | C2×#22575686, #39906237, C3×#22575686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8643, 3);