Finite Group DatabasebetaFinite Group Databasebeta| order | 3684 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C307⋊C3)⋊C4 |
| unambiguous semidirect product | Dic307⋊C3 |
| derived, Sylow | C307 ⋊ C3×C4 |
| Hall | Dic307 ⋊ C3 |
| Hall | C307⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D307⋊C3 |
| commutator, hypocenter | C307 | C3×C4 |
| Fitting, socle, cosocle | C2×C307 | C2×C3 |
| prime radical | C2×C307⋊C3 | C2 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 311 |
| transitive degree | μt(G) = 1228 |
Polycyclic presentation:
2,3,307,2|a^2=d,c^a=c^306,c^b=c^289114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3684, 2);