Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #3672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×#3674 |
| Sylow | C3×C9 ⋊ C2×Q16 |
218 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#3674, #13140652, #13140655, … |
| maximal normal subgroup of | Dic3×#3674, #13140652, #13140655, … |
| maximal quotient of | C2×C3×#63366, C3×#10588646, C2×C3×#63368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1620);