Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D8×#272 |
| Fitting | D8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×D8 |
418 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #13136927, #13136929, #13139239, … |
| maximal normal subgroup of | #13136927, #13136929, #13139239, … |
| maximal quotient of | #13143928, #13143929, #13143930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1759);