Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of (C3⋊#226)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×(C3⋊#226)⋊C3 |
| unambiguous semidirect product | (C2×C3⋊#226)⋊C3 |
161 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 161 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | #13146329, #13146334, #13146335, … |
| maximal normal subgroup of | #13146329, #13146334, #13146335, … |
| maximal quotient of | C4×(C3⋊#226)⋊C3, C4⋊((C3⋊#226)⋊C3), #10593625⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2315);