Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#5432 |
1945 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1945 conjugacy classes of subgroups — too many to draw. Only its 165 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 | C4×A4⋊SL(2,ℤ/4), C42×GL(2,ℤ/4), #72228394, … |
| maximal normal subgroup of | C42×GL(2,ℤ/4), #72228394, #72247723 |
| maximal quotient of | #72247723, #72253042 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1086067);