Finite Group DatabasebetaFinite Group Databasebeta| order | 8292 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic691 |
| derived, Sylow | C691 ⋊ C3×C4 |
| Hall | C3×C691 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D691 |
| commutator, hypocenter | C691 | C3×C4 |
| Frattini | C2 | C3×D691 |
| Fitting, socle | C2×C3×C691 | C2 |
| LCS | G ▷ C691 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
2082 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic691⋊C9, C9×Dic691, C3×(C691⋊C3)⋊C4, … |
| maximal normal subgroup of | Dic691⋊C9, C9×Dic691, C3×(C691⋊C3)⋊C4, … |
| maximal quotient of | C9×Dic691, C3×Dic2073, C32×Dic691 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8292, 5);