Finite Group DatabasebetaFinite Group Databasebeta| order | 27620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic1381⋊C5 |
| derived, Sylow | C1381 ⋊ C4×C5 |
| Hall | C1381⋊C5 ⋊ C4 |
| Hall | Dic1381 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1381⋊C5 |
| commutator, hypocenter | C1381 | C4×C5 |
| Fitting, socle, cosocle | C2×C1381 | C2×C5 |
| prime radical | C2×C1381⋊C5 | C2 |
| LCS | G ▷ C1381 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5524 |
Polycyclic presentation:
2,5,1381,2|a^2=d,c^a=c^1380,c^b=c^101296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27620, 2);