Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88860 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C33 |
| direct product | C2×#88863 |
| Sylow | C33 ⋊ C2×Q16 |
840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13161166, #13161167, #13161170, … |
| maximal normal subgroup of | #13161166, #13161167, #13161170, … |
| maximal quotient of | #13163602, C2×#11722177, C2×#11722180, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3951);