Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #733⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×#733⋊C2 |
| Fitting | C8×#733 ⋊ C2 |
| derived, Sylow | #733 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #733⋊C2 |
| commutator, hypocenter | #733 | C2×C8 |
| Frattini | C32×C4 | C2×C3⋊D3 |
| Fitting | C8×#733 | C2 |
| socle | C2×C3 | C4×#272 |
| prime radical | C2×#733⋊C2 | C4 |
| cosocle | C4×#733 | C22 |
| LCS | G ▷ #733 | |
| UCS | C1 ◁ C8 | |
143 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, 477);