Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
| direct product | D3×#6204 |
| unambiguous semidirect product | C3⋊(C2×#6204) |
201 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
93 conjugacy classes — view the full character table.
| maximal subgroup of | #72252998, #72253007, #72253010 |
| maximal normal subgroup of | #72252998 |
| maximal quotient of | #72253007 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2165);