Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D32×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | D32×S4 |
| unambiguous semidirect product | (C3×D3×S4)⋊C2 |
| unambiguous semidirect product | (C3⋊D3×S4)⋊C2 |
| unambiguous semidirect product | (D3×C3⋊S4)⋊C2 |
| Fitting, socle | C22×C32 ⋊ C22×D3 |
| derived | C32×A4 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×A4 | C23 |
| Fitting, socle | C22×C32 | C22×D3 |
| LCS | G ▷ C32×A4 | |
| UCS | C1 | |
605 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 605 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
45 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4673);