Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#88676 |
| Fitting | C22×C3×H(3,𝔽3) ⋊ C22 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×D4 |
537 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 537 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) = 72 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #72219732, C3×#13164262, #72222953, … |
| maximal normal subgroup of | #72219732, C3×D4×((C3⋊D3)⋊C3)⋊C2 |
| maximal quotient of | #72219727, C3×#13164262, #72259324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2331);