Finite Group DatabasebetaFinite Group Databasebeta| order | 732 |
| isoclinism | isoclinic class of D61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic61⋊C3 |
| derived, Sylow | C61 ⋊ C3×C4 |
| Hall | Dic61 ⋊ C3 |
| Hall | C61⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D61⋊C3 |
| commutator, hypocenter | C61 | C3×C4 |
| Fitting, socle, cosocle | C2×C61 | C2×C3 |
| prime radical | C2×C61⋊C3 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 244 |
Polycyclic presentation:
2,3,2,61|a^2=c,d^a=d^60,d^b=d^4732 conjugacy classes — view the full character table.
| maximal subgroup of | #92420⋊C3, (C61⋊C3)⋊Q8, C4×D61⋊C3, … |
| maximal normal subgroup of | #92420⋊C3, (C61⋊C3)⋊Q8, C4×D61⋊C3, … |
| maximal quotient of | #92418⋊C3, C2×Dic61⋊C3, Dic61⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(732, 1);