Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D3×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C24 |
| direct product | Dic3×C22⋊A4 |
| unambiguous semidirect product | C3⋊(C4×C22⋊A4) |
| derived | C24×C3 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C22⋊A4 |
| commutator, hypocenter | C24×C3 | C3×C4 |
| Fitting, socle, cosocle | C25×C3 | C2×C3 |
| prime radical | C2×C3×C22⋊A4 | C2 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C2 | |
538 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | #73846⋊C3, #73818⋊C3, Dic3×#120⋊C3, … |
| maximal normal subgroup of | #73846⋊C3, #73818⋊C3, Dic3×#120⋊C3, … |
| maximal quotient of | C3⋊C8×C22⋊A4, Dic3×C22⋊SL(2,𝔽3), C3⋊#85665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8514);