Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | Q8×C9⋊A4 |
| Fitting | C22×Q8×C9 ⋊ C3 |
| Sylow | C22×Q8 ⋊ 3−1+2 |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #3674⋊A4, #3675⋊A4, SD16×C9⋊A4, … |
| maximal normal subgroup of | #3674⋊A4, #3675⋊A4, SD16×C9⋊A4, … |
| maximal quotient of | C4⋊C4×C9⋊A4, #13152130, Q8×C9⋊SL(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2520);