Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#88676 |
| Fitting | C23×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ C22×D4 |
880 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | #13137470, #13148494, #13148495, … |
| maximal normal subgroup of | #13137470, #13148494, #13148495, … |
| maximal quotient of | C2×#11721101, C2×#11721079, C2×#11721119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2510);