Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×#984 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | #13146242, #13146247, #13146248, … |
| maximal normal subgroup of | #13146242, #13146247, #13146248, … |
| maximal quotient of | C9×#5386, C9×#5388, C9×C4⋊#226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2295);