Finite Group DatabasebetaFinite Group Databasebeta| order | 8643 |
| isoclinism | isoclinic class of C67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×C67⋊C3 |
| unambiguous semidirect product | C67⋊(C3×C43) |
| Fitting, socle, Hall | C43×C67 ⋊ C3 |
| derived, Sylow | C67 ⋊ C3×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C67⋊C3 |
| commutator, hypocenter | C67 | C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C43×C67 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C43 | |
8 conjugacy classes of subgroups.
1075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C43×C67⋊C3, C43×D67⋊C3, D43×C67⋊C3, … |
| maximal normal subgroup of | C2×C43×C67⋊C3, C43×D67⋊C3, D43×C67⋊C3, … |
| maximal quotient of | C2×C43×C67⋊C3, C43×C67⋊C9, C3×C43×C67⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8643, 2);