Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×SL(2,ℤ/4)⋊C4 |
1121 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 1121 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C42×GL(2,ℤ/4) |
| maximal normal subgroup of | C42×GL(2,ℤ/4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1086066);