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×C9⋊A4 |
| Fitting | C25×C9 ⋊ C3 |
| Sylow | C25 ⋊ 3−1+2 |
598 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #3676⋊A4, C22⋊C4×C9⋊A4, C22×Dic9⋊A4, … |
| maximal normal subgroup of | #3676⋊A4, C22⋊C4×C9⋊A4, C22×Dic9⋊A4, … |
| maximal quotient of | C22×C4×C9⋊A4, C2×D4×C9⋊A4, C23×C9⋊SL(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4035);