Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #66343 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4×C9 |
| direct product | C4×#66343 |
| Fitting | C4×C92 ⋊ C4 |
| derived, Sylow | C92 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #66343 |
| commutator, hypocenter | C92 | C42 |
| Frattini, socle | C2×C32 | C2×#157 |
| Fitting | C4×C92 | C4 |
| prime radical, cosocle | C2×C9⋊D9 | C22 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C4 | |
125 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 786);