Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×#6296 |
| Sylow | C34 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#1113 |
| commutator, Fitting, socle, cosocle | C2×C34 | C23 |
| prime radical | C2×C33×D3 | C22 |
| hypocenter | C34 | C2×Q8 |
| LCS | G ▷ C2×C34 ▷ C34 | |
| UCS | C1 ◁ C2 | |
555 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 555 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
81 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3253);