Finite Group DatabasebetaFinite Group Databasebeta| order | 6620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic331⋊C5 |
| unambiguous semidirect product | (C331⋊C5)⋊C4 |
| derived, Sylow | C331 ⋊ C4×C5 |
| Hall | C331⋊C5 ⋊ C4 |
| Hall | Dic331 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D331⋊C5 |
| commutator, hypocenter | C331 | C4×C5 |
| Fitting, socle | C2×C331 | C2×C5 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,331,2|a^2=d,c^a=c^330,c^b=c^6486 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6620, 2);