Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×C3⋊#6180 |
| unambiguous semidirect product | (C2×C3)⋊#6180 |
| derived, Sylow | C3×H(3,𝔽3) ⋊ C2×C8 |
546 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 243 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1731);