Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #4625 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#4625 |
| derived | C22⋊A4 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4625 |
| commutator, hypocenter | C22⋊A4 | C3×C4 |
| Frattini | C23 | C3×S4 |
| Fitting | C3×#120 | D3 |
| socle | C22×C3 | SL(2,ℤ/4) |
| prime radical | C3×#120⋊C3 | C2 |
| cosocle | #120⋊C3 | C2×C3 |
| LCS | G ▷ C22⋊A4 | |
| UCS | C1 ◁ C3 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
33 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4625, #4625⋊D3, C2×C3×#4625, … |
| maximal normal subgroup of | D3×#4625, #4625⋊D3, C2×C3×#4625, … |
| maximal quotient of | C3×#67998, C3×#68001, C3×#68002, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1985);