Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88790 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#88799 |
| Sylow | C33 ⋊ C2×Q16 |
512 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | #13155660, #13155663, #13155704, … |
| maximal normal subgroup of | #13155660, #13155663, #13155704, … |
| maximal quotient of | #13158857, #13158867, #13158887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3352);