Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #66365⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | C2×#66365⋊C2 |
| unambiguous semidirect product | #66365⋊C22 |
| unambiguous semidirect product | (C2×#66365)⋊C2 |
| Fitting | C23×3−1+2 ⋊ D3 |
| derived | #66365 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #66365⋊C2 |
| commutator, cosocle, hypocenter | #66365 | C22 |
| Frattini | C32 | C2×C3⋊S4 |
| Fitting | C23×3−1+2 | D3 |
| socle | C23×C3 | #272 |
| LCS | G ▷ #66365 | |
| UCS | C1 ◁ C2 | |
222 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
46 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1839);