Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C33 |
| direct product | C2×#89080 |
| Fitting | C2×C33×Q8 ⋊ C2 |
| Sylow | C33 ⋊ C2×#41 |
2296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #13161134, #13161142, #13161198, … |
| maximal normal subgroup of | #13161134, #13161142, #13161198, … |
| maximal quotient of | C2×#11723931, C2×#11723933, C2×#11723934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4648);