Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C33 |
| direct product | Q8×C3⋊(C3⋊Dic3) |
| Sylow | C33 ⋊ C4×Q8 |
980 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #13161160, #13161161, #13161162, … |
| maximal normal subgroup of | #13161160, #13161161, #13161162, … |
| maximal quotient of | C4⋊C4×C3⋊(C3⋊Dic3), #13163615, #13163619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3953);