Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q16×#272 |
| Fitting | Q16×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×Q16 |
330 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 330 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) = 144 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #13136931, #13136933, #13139277, … |
| maximal normal subgroup of | #13136931, #13136933, #13139277, … |
| maximal quotient of | #13143994, #13143996, #13143998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1773);