Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | Q8×C9×A4 |
| Fitting | C22×Q8×C9 ⋊ C3 |
| Sylow | C22×Q8 ⋊ C3×C9 |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#5416, C9×#5417, #13146972, … |
| maximal normal subgroup of | C9×#5416, C9×#5417, #13146972, … |
| maximal quotient of | C9×A4×C4⋊C4, C9×#557⋊C3, Q8×C9×SL(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2518);