Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#10619679 |
| Fitting | C23×AΣL(1,𝔽27) ⋊ C2 |
| Sylow | AΣL(1,𝔽27) ⋊ C2×D4 |
540 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
86 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×#4183, C2×C3×#10619679 |
| maximal normal subgroup of | C2×D4×#4183, C2×C3×#10619679 |
| maximal quotient of | C2×C3×#10619679 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1194);