Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C33 |
| direct product | D8×C3⋊(C3⋊D3) |
| Fitting | C33×D8 ⋊ C2 |
| Sylow | C33 ⋊ C2×D8 |
1064 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | #13160205, #13160211, #13160222, … |
| maximal normal subgroup of | #13160205, #13160211, #13160222, … |
| maximal quotient of | #13163396, #13163397, #13163398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3918);