Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C34 |
| direct product | C2×SL(2,𝔽3)×H(3,𝔽3) |
| Fitting | C2×Q8×H(3,𝔽3) ⋊ C3 |
| Sylow | C2×Q8 ⋊ C3×H(3,𝔽3) |
436 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72220368, C2×#13048389, C2×SL(2,𝔽3)×(C3⋊D3)⋊C3, … |
| maximal normal subgroup of | C2×#13048389, C2×SL(2,𝔽3)×(C3⋊D3)⋊C3, C2×#13048417, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2520);