Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88810 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#88811 |
| Sylow | C33 ⋊ C2×SD16 |
402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #13155637, #13155640, #13155643, … |
| maximal normal subgroup of | #13155637, #13155640, #13155643, … |
| maximal quotient of | #13161484, #13161485, #13161489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3629);