Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #733⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×#733⋊C2 |
| unambiguous semidirect product | #733⋊C24 |
| unambiguous semidirect product | (C2×#733)⋊C23 |
| Fitting | C23×#733 ⋊ C2 |
| derived, Sylow | #733 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #733⋊C2 |
| commutator, cosocle, hypocenter | #733 | C24 |
| Frattini | C32 | C23×C3⋊D3 |
| Fitting | C23×#733 | C2 |
| socle | C23×C3 | #272 |
| LCS | G ▷ #733 | |
| UCS | C1 ◁ C23 | |
871 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1920);