Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #66343 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C9 |
| direct product | C2×#10619526 |
| derived, Sylow | C92 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #66343 |
| commutator, hypocenter | C92 | C2×C8 |
| Frattini | C2×C32 | C2×#157 |
| Fitting | C22×C92 | C4 |
| socle, prime radical | C22×C32 | #157 |
| cosocle | C9⋊Dic9 | C22 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C22 | |
113 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 788);