Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4⋊C4×GL(2,𝔽3) |
| Fitting | Q8×C4⋊C4 ⋊ D3 |
695 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 695 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 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C4⋊C4×AGL(2,𝔽3) |
| maximal quotient of | C4⋊C4×AGL(2,𝔽3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087400);