Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D3×A42 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | D3×A42 |
| unambiguous semidirect product | C3⋊(C2×A42) |
| unambiguous semidirect product | (C22×D3×A4)⋊C3 |
| unambiguous semidirect product | (D3×C22⋊A4)⋊C3 |
| Fitting, socle, derived | C24×C3 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C24×C3 | C2×C32 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 | |
282 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×A4×S4, D3×#1020⋊C3, D3×A4⋊S4, … |
| maximal normal subgroup of | D3×A4×S4, D3×#1020⋊C3, D3×A4⋊S4, … |
| maximal quotient of | A4×C3⋊(#41⋊C3), D3×A4×SL(2,𝔽3), C3⋊((#41⋊C3)⋊A4), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4680);