Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#64307 |
| Fitting | C2×C33×C4 ⋊ C22 |
| Sylow | C33 ⋊ H(5,𝔽2) |
814 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | #13155903, #13155904, #13155906, … |
| maximal normal subgroup of | #13155903, #13155904, #13155906, … |
| maximal quotient of | C3×#10593887, C3×#10593889, C3×#10593900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4502);