Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of ((C22⋊C9)⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C22 |
| derived | C22⋊C9 ⋊ C22×C9 |
192 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | #72229373, C2×#72220166, C2×#14517984 |
| maximal normal subgroup of | #72229373, C2×#14517984 |
| maximal quotient of | C2×#11757417⋊C2, #72229373, C2×#72220166 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1819);