Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D9×ΓL(1,𝔽25) |
| Fitting | C3×C8×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×M16 |
224 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D9×ΓL(1,𝔽25), D9×#901, #13149746, … |
| maximal normal subgroup of | C2×D9×ΓL(1,𝔽25), D9×#901, #13149746, … |
| maximal quotient of | #13138115, #13138117, #13138119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 766);