Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
| direct product | H(3,𝔽3)×GL(2,𝔽3) |
| unambiguous semidirect product | (C32×GL(2,𝔽3))⋊C3 |
| Fitting | Q8×H(3,𝔽3) ⋊ D3 |
227 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | GL(2,𝔽3)×(C3⋊D3)⋊C3, GL(2,𝔽3)×#272 |
| maximal normal subgroup of | GL(2,𝔽3)×(C3⋊D3)⋊C3, GL(2,𝔽3)×#272 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2081);