Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×Dic27 |
| Sylow | C27 ⋊ C4×Q8 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #13134294, #13134297, #13134300, … |
| maximal normal subgroup of | #13134294, #13134297, #13134300, … |
| maximal quotient of | C4⋊C4×Dic27, #13134485, #13134489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 161);