Finite Group DatabasebetaFinite Group Databasebeta| order | 1220 |
| isoclinism | isoclinic class of D61⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic61⋊C5 |
| derived, Sylow | C61 ⋊ C4×C5 |
| Hall | C61⋊C5 ⋊ C4 |
| Hall | Dic61 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D61⋊C5 |
| commutator, hypocenter | C61 | C4×C5 |
| Fitting, socle, cosocle | C2×C61 | C2×C5 |
| prime radical | C2×C61⋊C5 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 244 |
Polycyclic presentation:
2,5,2,61|a^2=c,d^a=d^60,d^b=d^932 conjugacy classes — view the full character table.
| maximal subgroup of | (Dic61⋊C3)⋊C5, C3×Dic61⋊C5, C3⋊(Dic61⋊C5), … |
| maximal normal subgroup of | (Dic61⋊C3)⋊C5, C3×Dic61⋊C5, C11×Dic61⋊C5, … |
| maximal quotient of | C3×Dic61⋊C5, C3⋊(Dic61⋊C5), #14555575⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1220, 1);