Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23 |
| direct product | Q8×#997 |
| Fitting, Sylow | Q8×H(5,𝔽2) ⋊ C3 |
1391 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 1391 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
55 conjugacy classes — view the full character table.
| derived subgroup of | SL(2,𝔽3)×#5934 |
| maximal subgroup of | SL(2,𝔽3)×#997, SD16×#997, Q8×#5934, … |
| maximal normal subgroup of | SL(2,𝔽3)×#997, SD16×#997, Q8×#5934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085168);