Finite Group DatabasebetaFinite Group Databasebeta| order | 1698 |
| isoclinism | isoclinic class of D283⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D283⋊C3 |
| unambiguous semidirect product | (C283⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C283 ⋊ C2×C3 |
| Hall | C283⋊C3 ⋊ C2 |
| Hall | D283 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C283 | C2×C3 |
| LCS | G ▷ C283 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 283 |
| transitive degree | μt(G) = 283 |
Polycyclic presentation:
2,3,283|c^a=c^282,c^b=c^23853 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D283⋊C3, C7×D283⋊C3, #26045220, … |
| maximal normal subgroup of | C2×D283⋊C3, C7×D283⋊C3, C11×D283⋊C3, … |
| maximal quotient of | (C283⋊C3)⋊C4, C2×D283⋊C3, C7×D283⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1698, 1);