Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#73141 |
1577 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1577 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×A4⋊(A4⋊C8), C2×C8×GL(2,ℤ/4), #72247723, … |
| maximal normal subgroup of | C2×C8×GL(2,ℤ/4), #72247723, #72267949, … |
| maximal quotient of | #72253102 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1086969);