Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | Q8×#1094 |
| Sylow | C22×Q8 ⋊ 3−1+2 |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #10589518⋊C3, #10589519⋊C3, SD16×#1094, … |
| maximal normal subgroup of | #10589518⋊C3, #10589519⋊C3, SD16×#1094, … |
| maximal quotient of | C4⋊C4×#1094, #13152200, Q8×#6204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2536);