Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C23 |
| direct product | C9×#1020 |
| Fitting | C24×C9 ⋊ D3 |
| derived | C22⋊A4 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #1020 |
| commutator, hypocenter | C22⋊A4 | C2×C9 |
| Frattini | C3 | C3×#1020 |
| Fitting | C24×C9 | D3 |
| socle | C24×C3 | C3×D3 |
| prime radical | C3×#1020 | C3 |
| cosocle | C3×C22⋊A4 | C2×C3 |
| LCS | G ▷ C22⋊A4 | |
| UCS | C1 ◁ C9 | |
182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #13146262, C9×#1020⋊C2, D9×#1020, … |
| maximal normal subgroup of | #13146262, C9×#1020⋊C2, D9×#1020, … |
| maximal quotient of | C9×#5930, C9×#5931, C9×#5932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4016);