Finite Group DatabasebetaFinite Group Databasebeta| order | 8292 |
| automorphism | Aut(G) order 5721480 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2073 |
| unambiguous semidirect product | C3⋊Dic691 |
| unambiguous semidirect product | C691⋊Dic3 |
| derived, Hall | C3×C691 ⋊ C4 |
| Sylow | C691 ⋊ Dic3 |
| Sylow | C3 ⋊ Dic691 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2073 |
| commutator, hypocenter | C3×C691 | C4 |
| Fitting, socle | C2×C3×C691 | C2 |
| LCS | G ▷ C3×C691 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,691,2|a^2=d,b^a=b^2,c^a=c^6902076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic6219, C3⋊((C691⋊C3)⋊C4), C3⋊Dic2073, … |
| maximal normal subgroup of | C3⋊((C691⋊C3)⋊C4), C3×Dic2073, Dic4146 |
| maximal quotient of | Dic6219, C3⋊Dic2073, C3×Dic2073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8292, 6);