Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of A4×PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×PSU(3,𝔽2) |
| Fitting, socle | C22×C32 ⋊ C3×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C22×C3⋊D3 | C22×C3 |
| Fitting, socle, hypocenter | C22×C32 | C3×Q8 |
| prime radical | A4×C3⋊D3 | C22 |
| LCS | G ▷ C22×C3⋊D3 ▷ C22×C32 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
24 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4672);