Finite Group DatabasebetaFinite Group Databasebeta| order | 3678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D613 |
| Fitting, socle, Hall | C3×C613 ⋊ C2 |
| derived, Sylow | C613 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D613 |
| commutator, cosocle, hypocenter | C613 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C613 | C2 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 616 |
| transitive degree | μt(G) = 1839 |
924 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #19149450⋊C2, C9×D613, C3×D613⋊C3, … |
| maximal normal subgroup of | #19149450⋊C2, C9×D613, C3×D613⋊C3, … |
| maximal quotient of | C9×D613, C3×D1839, C32×D613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3678, 4);