Finite Group DatabasebetaFinite Group Databasebeta| order | 3678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D613⋊C3 |
| unambiguous semidirect product | (C613⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C613 ⋊ C2×C3 |
| Hall | C613⋊C3 ⋊ C2 |
| Hall | D613 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C613 | C2×C3 |
| LCS | G ▷ C613 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 613 |
| transitive degree | μt(G) = 613 |
Polycyclic presentation:
2,3,613|c^a=c^612,c^b=c^65108 conjugacy classes — view the full character table.
| maximal subgroup of | #19149452⋊C2, C3×D613⋊C3, C3⋊(D613⋊C3), … |
| maximal normal subgroup of | #19149452⋊C2, C3×D613⋊C3, C5×D613⋊C3, … |
| maximal quotient of | #19149450⋊C2, C3×D613⋊C3, C3⋊(D613⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3678, 1);