Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D3×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
| direct product | Dic3×SL(2,ℤ/4) |
| derived | C3×A4 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×S4 |
| commutator, hypocenter | C3×A4 | C42 |
| Fitting, socle | C24×C3 | C2×D3 |
| prime radical, cosocle | C22×C3×A4 | C22 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C22 | |
266 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | Dic6×SL(2,ℤ/4), #11921882, Dic3×A4⋊Q8, … |
| maximal normal subgroup of | Dic6×SL(2,ℤ/4), #11921882, Dic3×A4⋊Q8, … |
| maximal quotient of | Dic3×A4⋊C8, #11920612, C3⋊C8×SL(2,ℤ/4), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5119);