Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊(D27⋊C3) |
| unambiguous semidirect product | (C2×D108)⋊C3 |
| Fitting | C2×C4×C27⋊C3 ⋊ C2 |
| Sylow | C27⋊C3 ⋊ C2×D4 |
232 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×D27⋊C3, #72276045, #72276094, … |
| maximal normal subgroup of | C2×D4×D27⋊C3, #72276045, #72276094, … |
| maximal quotient of | #72276094, #72276189 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1027);