Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×#1088 |
| Fitting | Q8×H(3,𝔽3) ⋊ C4 |
| Sylow | H(3,𝔽3) ⋊ C4×Q8 |
181 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | Q8⋊#6249, #13146649, #13146651, … |
| maximal normal subgroup of | Q8⋊#6249, #13146649, #13146651, … |
| maximal quotient of | #13147339, #13147340, #13147341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2419);