Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C33 |
| direct product | C2×Q8×C3⋊(C3⋊D3) |
| Fitting | C2×C33×Q8 ⋊ C2 |
| Sylow | C33 ⋊ C22×Q8 |
2184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #13161132, #13161144, #13161196, … |
| maximal normal subgroup of | #13161132, #13161144, #13161196, … |
| maximal quotient of | C2×#11723928, C2×#11723937, C2×#11723929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4647);