Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊D3×#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C32 |
| direct product | C3⋊D3×#622 |
| derived, Sylow | C34 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D3×#157 |
| commutator, hypocenter | C34 | C2×C8 |
| Fitting, socle | C2×C34 | C2×C4 |
| prime radical | C2×C32×C3⋊D3 | C4 |
| cosocle | C32×C3⋊Dic3 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3116);