Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24 |
| direct product | C23×#1094 |
| Sylow | C25 ⋊ 3−1+2 |
940 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #10589534⋊C3, C22⋊C4×#1094, C22×#1094⋊C4, … |
| maximal normal subgroup of | #10589534⋊C3, C22⋊C4×#1094, C22×#1094⋊C4, … |
| maximal quotient of | C22×C4×#1094, C2×D4×#1094, C23×#6204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4037);