Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6226 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×#88551 |
| Sylow | C3×C9 ⋊ C2×C22⋊C4 |
660 conjugacy classes of subgroups; only the 281 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 281 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13135217, #13135218, #13135219, … |
| maximal normal subgroup of | #13135217, #13135218, #13135219, … |
| maximal quotient of | C2×#11720571, #13144797, C2×#11720572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1840);