Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | Q8×C22⋊H(3,𝔽3) |
| Fitting | C22×C32×Q8 ⋊ C3 |
| Sylow | C22×Q8 ⋊ H(3,𝔽3) |
264 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #10593650⋊C3, #10593651⋊C3, #13147057, … |
| maximal normal subgroup of | #10593650⋊C3, #10593651⋊C3, #13147057, … |
| maximal quotient of | C4⋊C4×C22⋊H(3,𝔽3), #557⋊H(3,𝔽3), Q8×Q8⋊H(3,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2538);