Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C25 |
| direct product | C9×#1004 |
| Fitting | C2×C3×D4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ H(5,𝔽2) |
552 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 255 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
243 conjugacy classes — view the full character table.
| maximal subgroup of | #13140439, #13140440, #13140445, … |
| maximal normal subgroup of | #13140439, #13140440, #13140445, … |
| maximal quotient of | C9×#5483, C9×#5486, C9×#5490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2579);