Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6189 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#88420 |
| Sylow | C3×C9 ⋊ C2×M16 |
226 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | #13137208, #13137209, #13137211, … |
| maximal normal subgroup of | #13137208, #13137209, #13137211, … |
| maximal quotient of | #13137023, #13137024, #13137114, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 846);