Finite Group DatabasebetaFinite Group Databasebeta| order | 8196 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic683 |
| unambiguous semidirect product | C683⋊(C3×C4) |
| derived, Sylow | C683 ⋊ C3×C4 |
| Hall | C3×C683 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D683 |
| commutator, hypocenter | C683 | C3×C4 |
| Frattini | C2 | C3×D683 |
| Fitting, socle | C2×C3×C683 | C2 |
| LCS | G ▷ C683 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
2058 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic683, C3×Dic2049, C32×Dic683 |
| maximal normal subgroup of | C9×Dic683, C32×Dic683 |
| maximal quotient of | C9×Dic683, C3×Dic2049, C32×Dic683 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8196, 3);