Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of C3⋊#226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊GU(2,𝔽3) |
| unambiguous semidirect product | (C2×C3)⋊GU(2,𝔽3) |
| derived | C3×SL(2,𝔽3) ⋊ C2×C4 |
200 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 200 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 | Dic3×GU(2,𝔽3), #11920682, Dic3⋊GU(2,𝔽3), … |
| maximal normal subgroup of | Dic3×GU(2,𝔽3), #11920682, Dic3⋊GU(2,𝔽3), … |
| maximal quotient of | C2×C3⋊(SL(2,𝔽3)⋊C8), #11921013, C4×C3⋊GU(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5538);