Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#3699 |
| Fitting | D4×C92 ⋊ C2 |
| Sylow | C92 ⋊ #41 |
236 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72219896, C9×#63710, #72219950, … |
| maximal normal subgroup of | #72219896, C9×#63710, #72219950, … |
| maximal quotient of | C2×C9×#3699 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1054);