Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×#4208 |
| Fitting | C2×C4×#737 ⋊ C2 |
| Sylow | #737 ⋊ C22×C4 |
523 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 523 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
240 conjugacy classes — view the full character table.
| automorphism group of | C3×C5×C27 |
| outer automorphism group of | C3×C5×C27 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2624);