Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#379 ⋊ D3 |
1070 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 1070 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^4,3,2^4|b^2=c,b^a=bd,e^a=e^2,f^a=fg,h^a=hi,f^b=fh,g^b=gi,f^e=g,g^e=fg,h^e=i,i^e=hi44 conjugacy classes — view the full character table.
| maximal subgroup of | #72215370, #72215795, #72215806, … |
| maximal normal subgroup of | #72215370, #72215795, #72215806, … |
| maximal quotient of | #72220366, #72243137, #72252360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085712);