Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C32×Q8×A4 |
| Fitting | C22×C32×Q8 ⋊ C3 |
| Sylow | C22×Q8 ⋊ C33 |
468 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#5416, C32×#5417, C3×#10593650, … |
| maximal normal subgroup of | C32×#5416, C32×#5417, C3×#10593650, … |
| maximal quotient of | C32×A4×C4⋊C4, C32×#557⋊C3, C32×Q8×SL(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4604);