Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q16×D27 |
| Fitting | Q16×C27 ⋊ C2 |
| Sylow | C27 ⋊ C2×Q16 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D27, #13134420, Q32×D27, … |
| maximal normal subgroup of | SD32×D27, #13134420, Q32×D27, … |
| maximal quotient of | #13134295, #13134297, #13134299, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 133);