Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C8×GL(2,𝔽3) |
| Fitting | C2×C8×Q8 ⋊ D3 |
| derived | SL(2,𝔽3) ⋊ C22×C8 |
561 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 561 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C8×AGL(2,𝔽3), #97×GL(2,𝔽3) |
| maximal normal subgroup of | #97×GL(2,𝔽3) |
| maximal quotient of | C2×C8×AGL(2,𝔽3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1086205);