Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #64214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×#64218 |
| Sylow | C33 ⋊ M32 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #13165066, #13165067, C3×#10593168, … |
| maximal normal subgroup of | #13165066, #13165067, C3×#10593168, … |
| maximal quotient of | C3×#10593263, C3×#10593265, C3×C22⋊#3771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4202);