Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D3×C3⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | D3×C3⋊#157 |
| unambiguous semidirect product | (C3×D3)⋊#157 |
| Fitting, socle, derived, Sylow | C34 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C34 | C2×C4 |
| prime radical | C3×D3×C3⋊D3 | C2 |
| cosocle | C32×C3⋊D3 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 | |
160 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
36 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#157, D3×D32⋊D3, D3×C3⋊PSU(3,𝔽2), … |
| maximal normal subgroup of | D32×#157, D3×D32⋊D3, D3×C3⋊PSU(3,𝔽2), … |
| maximal quotient of | Dic3×C3⋊#157, (C2×D3)⋊(C3⋊#157), Dic3⋊(C3⋊#157), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 714);