Finite Group DatabasebetaFinite Group Databasebeta| order | 3678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×C613⋊C3 |
| unambiguous semidirect product | (C2×C613)⋊C3 |
| Fitting, socle, Hall | C2×C613 ⋊ C3 |
| derived, Sylow | C613 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C613⋊C3 |
| commutator, cosocle, hypocenter | C613 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C613 | C3 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 615 |
| transitive degree | μt(G) = 1226 |
414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#19149452, D3×C613⋊C3, C2×C3×C613⋊C3, … |
| maximal normal subgroup of | C2×#19149452, C2×C3×C613⋊C3, C2×C5×C613⋊C3, … |
| maximal quotient of | C2×#19149450, D3×C613⋊C3, C2×C3×C613⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3678, 2);