Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D3×#859 |
| derived | C3×SL(2,𝔽3) ⋊ C2×C4 |
205 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5386, #11921673, #11921674, … |
| maximal normal subgroup of | D3×#5386, #11921673, #11921674, … |
| maximal quotient of | D3×SL(2,𝔽3)⋊C8, #11920560, Dic3×#859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5098);