Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #66343⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#66343⋊C2 |
| unambiguous semidirect product | #66343⋊C22 |
| unambiguous semidirect product | D92⋊C22 |
| Fitting | C2×C92 ⋊ D4 |
| Sylow | C92 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #66343⋊C2 |
| commutator, cosocle | C9⋊D9 | C23 |
| Frattini | C32 | C2×GO+(4,𝔽2) |
| Fitting | C2×C92 | D4 |
| socle | C2×C32 | GO+(4,𝔽2) |
| hypocenter | C92 | C2×D4 |
| LCS | G ▷ C9⋊D9 ▷ C92 | |
| UCS | C1 ◁ C2 | |
187 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1813);