Finite Group DatabasebetaFinite Group Databasebeta| order | 732 |
| isoclinism | isoclinic class of C3⋊#6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#6923 |
| Fitting, socle, derived, Hall | C3×C61 ⋊ C4 |
| Sylow | C61 ⋊ Dic3 |
| Sylow | C3 ⋊ #6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C61 | C4 |
| prime radical, cosocle | C3×D61 | C2 |
| LCS | G ▷ C3×C61 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 183 |
Polycyclic presentation:
2^2,3,61|a^2=b,c^a=c^2,d^a=d^11,d^b=d^6051 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6923, C2×C3⋊#6923, C9⋊#6923, … |
| maximal normal subgroup of | D3×#6923, C2×C3⋊#6923, C3⋊(#6923⋊C3), … |
| maximal quotient of | C3⋊#92420, C2×C3⋊#6923, C9⋊#6923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(732, 10);