Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×3−1+2⋊C4 |
| Sylow | 3−1+2 ⋊ C4×Q8 |
229 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 229 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #10588471⋊C3, #10588473⋊C3, #10588476⋊C3, … |
| maximal normal subgroup of | #10588471⋊C3, #10588473⋊C3, #10588476⋊C3, … |
| maximal quotient of | C4⋊C4×3−1+2⋊C4, #10588660⋊C3, #10588664⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1645);