Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#88722 |
| Fitting | C2×Q8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×#41 |
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #13140906, #13140917, #13140919, … |
| maximal normal subgroup of | #13140906, #13140917, #13140919, … |
| maximal quotient of | C2×#64099⋊C3, C2×#64101⋊C3, C2×#64102⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2593);